Darren Barr stabbed home the opener and Rudi Skacel's deflected shot gave Hearts a 2-0 lead before James McPake pulled one back for Hibs on 41 minutes.
Pa Kujabi's foul on Suso Santana led to a second booking for the former and a Hearts penalty, which was converted by Danny Grainger just after half-time.
Ryan McGowan's header and Skacel's second rounded off Hearts' win.
An eighth Scottish Cup triumph for the Tynecastle side, who had already qualified for the Europa League through the Scottish Premier League, ensures Hibs' long wait to add to their last win in the tournament in 1902 continues.
And St Johnstone, who finished one place behind Hearts in the league, are also beneficiaries of the result as they too now qualify for Europe.
Hearts, who left Craig Beattie on the bench and David Templeton out of the squad altogether, were forceful early on and Skacel, a scorer in the 2006 final, headed wide from Andrew Driver's cross.
And Paulo Sergio's side moved into a 15th-minute lead with a scrappy goal from Grainger's corner.
Hibs were unable to clear as Andy Webster and McGowan tried to force the issue and then McGowan's deflected shot sat up kindly for Barr to poke home.
Hearts' confidence grew and their use of the ball was stretching Hibs, who had Kujabi booked for a foul on Suso.
Skacel received Ian Black's pass just outside the box and his shot on the turn took a nick off McPake as it swerved past Mark Brown and doubled Hearts' advantage on 27 minutes.
Pat Fenlon's side had the chance to reduce their deficit when Kujabi's cross bounced up for O'Connor in front of goal but the striker snatched at his shot and cleared the bar.
McPake denied Hearts a third with a crucial clearance near the goal-line after Suso's shot had beaten Brown.
And the on-loan Coventry defender then made a vital contribution at the other end to give Hibs hope.
Tom Soares' poor corner was cleared but Hibs recycled the ball back to the midfielder on the right and his dangerous low delivery into a crowded area was nudged past keeper Jamie MacDonald by the outstretched foot of McPake.
Referee Craig Thomson showed leniency after Leigh Griffiths pushed Black as the two became involved in a scuffle, the Hibs striker perhaps still smarting from a heavy aerial challenge by the midfielder earlier in the match.
Half-time soon came and went and there was drama seconds after the restart as Hearts were awarded a penalty.
Kujabi pulled the jersey and caught the heel of Suso as the Hearts winger sped along the byeline and the Spaniard tumbled as he made his way into the box.
Thomson pointed to the spot but television replays suggested the foul by Kujabi had taken place just outside the box as the dismissed left-back trudged off the park in dejection.
Grainger calmly swept the ball home from 12 yards for his first Hearts goal.
Hibs' struggle to contain their opponents at set pieces continued as McGowan nodded over the line after Brown had got a hand on Stephen Elliott's initial header.
It got worse for the Leith side when Skacel found space in the D and sent another net-bound shot past Brown.
Black waved goodbye to the Hearts fans as his final appearance for the club came to an end five minutes from time, the midfielder replaced by Scott Robinson.
And within moments the Hearts fans were given the signal to start the celebrations as Thomson brought proceedings to a close.
Full Time   The referee signals the end of the game.
The official flags Eoin Doyle offside. Free kick taken by Jamie MacDonald.
Mark Brown restarts play with the free kick.
Substitution      Scott Robinson joins the action as a substitute, replacing Ian Black.
Inswinging corner taken right-footed by Ian Black from the right by-line, Foul by Andy Webster on James McPake, free kick awarded.
The ball is swung over by Ryan McGowan, blocked by Eoin Doyle.
Andy Webster takes the direct free kick.
Substitution      Mehdi Taouil comes on in place of Andrew Driver.
Free kick awarded for a foul by Ivan Sproule on Daniel Grainger.
Andrew Driver has an effort at goal from just outside the box which goes wide of the right-hand post.
Stephen Elliott produces a right-footed shot from just outside the penalty area that goes harmlessly over the target.
The ball is sent over by Leigh Griffiths, Jamie MacDonald makes a save.
Substitution      George Francomb is brought on as a substitute for Tom Soares.
Substitution      Suso Santana goes off and Craig Beattie comes on.
Suso Santana provided the assist for the goal.
Goal!  - Rudi Skacel -    Hibernian 1 - 5 Hearts        Rudi Skacel finds the net with a goal from just inside the area to the bottom right corner of the goal. Hibernian 1-5 Hearts.
Corner from the right by-line taken by Andy Webster, Headed effort from inside the penalty area by Darren Barr misses to the right of the target.
The ball is sent over by Ryan McGowan, clearance by Eoin Doyle.
The referee blows for offside. Eoin Doyle restarts play with the free kick.
Inswinging corner taken right-footed by Daniel Grainger from the right by-line.
Ryan McGowan sends in a cross, save made by Jamie MacDonald.
Free kick awarded for an unfair challenge on Daniel Grainger by Ivan Sproule. Jamie MacDonald takes the direct free kick.
James McPake delivers the ball, clearance made by Ryan McGowan.
Inswinging corner taken right-footed by Leigh Griffiths played to the near post, Andy Webster makes a clearance.
Leigh Griffiths takes a shot. Blocked by Andy Webster.
The ball is delivered by Rudi Skacel, Lewis Stevenson manages to make a clearance.
A cross is delivered by Leigh Griffiths, Ryan McGowan makes a clearance.
Substitution      Eoin Doyle is brought on as a substitute for Garry O'Connor.
Ian Black delivers the ball from the free kick right-footed from left wing, clearance made by James McPake.
Booking      Matt Doherty receives a yellow card for unsporting behaviour.
Andrew Driver fouled by Matt Doherty, the ref awards a free kick.
Corner from the right by-line taken by Ian Black, Header by Marius Zaliukas from deep inside the penalty area misses to the right of the target.
Stephen Elliott provided the assist for the goal.
Goal!  - Ryan McGowan -    Hibernian 1 - 4 Hearts        Ryan McGowan finds the back of the net with a headed goal from inside the six-yard box. Hibernian 1-4 Hearts.
Corner taken right-footed by Daniel Grainger to the near post,
Andrew Driver produces a cross, Matt Doherty gets a block in.
Garry O'Connor produces a  right-footed shot from deep inside the penalty area which goes wide of the right-hand post.
The assist for the goal came from Suso Santana.
Goal!  - Daniel Grainger -    Hibernian 1 - 3 Hearts        Daniel Grainger scores a placed penalty. Hibernian 1-3 Hearts.
Dismissal      Pa Saikou Kujabi dismissed for second bookable offence.
Penalty awarded for a foul by Pa Saikou Kujabi on Suso Santana.
The second half kicks off.
Half Time    The first half comes to an end.
Ivan Sproule sends in a cross, Daniel Grainger gets a block in.
Foul by Stephen Elliott on James McPake, free kick awarded. Free kick taken by Mark Brown.
Ian Black challenges Leigh Griffiths unfairly and gives away a free kick. The free kick is swung in right-footed by Tom Soares, save made by Jamie MacDonald.
Free kick awarded for a foul by Stephen Elliott on Paul Hanlon. James McPake takes the free kick.
Foul by Andy Webster on Garry O'Connor, free kick awarded. Tom Soares crosses the ball from the free kick right-footed from left channel, clearance by Ryan McGowan.
Substitution      Ivan Sproule on for Jorge Claros.
Tom Soares provided the assist for the goal.
Goal!  - James McPake -    Hibernian 1 - 2 Hearts        James McPake scores a goal from inside the six-yard box to the bottom left corner of the goal. Hibernian 1-2 Hearts.
Centre by Tom Soares,
Outswinging corner taken by Tom Soares from the right by-line played to the near post.
A cross is delivered by Lewis Stevenson, Effort from 12 yards by Leigh Griffiths. Blocked by Daniel Grainger.
The ball is crossed by Darren Barr.
A cross is delivered by Ryan McGowan.
Free kick awarded for a foul by Leigh Griffiths on Jamie MacDonald. Jamie MacDonald takes the direct free kick.
Darren Barr takes a shot. Save by Mark Brown.
Outswinging corner taken right-footed by Darren Barr, clearance made by Tom Soares.
Effort from 12 yards by Suso Santana. Blocked by James McPake.
Andrew Driver crosses the ball, clearance by Paul Hanlon.
Outswinging corner taken from the left by-line by Daniel Grainger, Garry O'Connor makes a clearance.
The ball is swung over by Andrew Driver, James McPake manages to make a clearance.
Pa Saikou Kujabi delivers the ball, Effort on goal by Garry O'Connor from inside the penalty area goes harmlessly over the bar.
The ball is swung over by Marius Zaliukas, clearance made by Matt Doherty.
Free kick awarded for a foul by Isaiah Osbourne on Ian Black. Daniel Grainger delivers the ball from the free kick left-footed from right wing, clearance by Matt Doherty.
The assist for the goal came from Ian Black.
Goal!  - Rudi Skacel -    Hibernian 0 - 2 Hearts        A goal is scored by Rudi Skacel from just inside the area to the bottom right corner of the goal. Hibernian 0-2 Hearts.
Centre by Daniel Grainger, clearance made by Isaiah Osbourne.
Free kick awarded for an unfair challenge on Stephen Elliott by James McPake. Free kick taken by Daniel Grainger.
The offside flag is raised against Rudi Skacel. Free kick taken by Mark Brown.
Darren Barr delivers the ball, clearance by James McPake.
Ian Black fouled by Jorge Claros, the ref awards a free kick. Daniel Grainger takes the free kick.
Isaiah Osbourne challenges Daniel Grainger unfairly and gives away a free kick. Jamie MacDonald restarts play with the free kick.
Foul by Rudi Skacel on Lewis Stevenson, free kick awarded. Free kick crossed by Leigh Griffiths.
The ball is crossed by Andrew Driver.
Shot by Andy Webster. Save by Mark Brown.
The free kick is delivered left-footed by Daniel Grainger from right wing, clearance by Matt Doherty.
Booking      The referee shows Pa Saikou Kujabi a yellow card for unsporting behaviour.
Free kick awarded for a foul by Pa Saikou Kujabi on Suso Santana.
Tom Soares takes the outswinging corner, clearance by Darren Barr.
Pa Saikou Kujabi fouled by Suso Santana, the ref awards a free kick. The free kick is swung in right-footed by Tom Soares, save by Jamie MacDonald.
Ryan McGowan provided the assist for the goal.
Goal!  - Darren Barr -    Hibernian 0 - 1 Hearts        Darren Barr scores a goal from deep inside the penalty area low into the middle of the goal. Hibernian 0-1 Hearts.
Ryan McGowan takes a shot. Blocked by Matt Doherty.
Outswinging corner taken from the right by-line by Daniel Grainger.
The ball is sent over by Andrew Driver, Matt Doherty gets a block in.
Garry O'Connor challenges Ian Black unfairly and gives away a free kick. Direct free kick taken by Ian Black.
Centre by Andrew Driver.
The referee blows for offside. Andy Webster takes the free kick.
The ball is swung over by Daniel Grainger, clearance made by Paul Hanlon. Leigh Griffiths fouled by Ian Black, the ref awards a free kick. Mark Brown restarts play with the free kick.
Free kick awarded for an unfair challenge on Suso Santana by Lewis Stevenson. Direct free kick taken by Daniel Grainger.
The assistant referee signals for offside against Leigh Griffiths.  Free kick taken by Jamie MacDonald.
Free kick awarded for an unfair challenge on Suso Santana by Isaiah Osbourne. Jamie MacDonald takes the direct free kick.
Foul by Stephen Elliott on James McPake, free kick awarded. Mark Brown takes the direct free kick.
Unfair challenge on Marius Zaliukas by Isaiah Osbourne results in a free kick. Marius Zaliukas takes the direct free kick.
The ref blows the whistle to begin the match.
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Hearts hammered Edinburgh rivals Hibernian to claim the Scottish Cup in a goal-laden Hampden final.