Lonsana Doumbouya headed Inverness ahead against the run of play, but Kenny McLean's free-kick levelled.
Jonny Hayes long run was halted by Gary Warren, earning the Dons a penalty, which Adam Rooney dispatched to put them ahead.
McLean sealed the points when Hayes was influential again, picking out the Dons midfielder on the counter attack.
Celtic's seemingly unassailable lead at the top suggests Aberdeen's best hope in league terms is to finish second once again.
This second successive away win was an important step with a number of sides bunched within striking distance before kick off.
They started well but fell behind to Inverness' first chance of the match. Ross Draper supplied an accurate ball which Doumbouya attacked and brilliantly glanced into the corner.
Defensively, Derek Mcinnes might feel his back line should have dealt with the cross, but the finish was one of real quality.
Aberdeen won a free-kick in a central area which McLean hit firmly and on target. It found the net with goalkeeper Owain Fon Williams perhaps a touch slow to react given it sped past well inside the post.
Hayes created the second with direct, determined play which took him into the box at speed.
Warren mistimed it and clearly caught the winger. Rooney doesn't miss many penalties and this one was perfect, straight in the corner despite Fon Williams anticipating the direction of the ball.
Andrew Considine thought he'd added a third but saw Fon Willaims produce an outstanding close range save to deny a more comfortable passage to the points.
James Maddison also came very close with an excellent free kick that struck the base of the post.
The third eventually arrived with Inverness pressing. Hayes broke at speed, played in McLean and he sealed the points with Fon Williams exposed.
It's a positive result and a good way to enter a big week for the club with the League Cup final against Celtic to follow.
The balance between attacking threat and defensive solidity is something Inverness might improve on.
In an attacking sense they are a real threat. Doumbouya is a real handful and when a chance comes, he has the confidence and composure to take it.
A commitment to attack sometimes leaves them exposed, which one league clean sheet demonstrates.
Doumbouya was unlucky to see one header loop narrowly over. Draper then was so unlucky with a brilliant run which he narrowly failed to convert.
Richie Foran's side have shown they can match the best of the Premiership at home this season, and despite dropping to just two points clear of bottom, you'd think they have enough to start climbing again.
Inverness manager Richie Foran: "We scored against the run of play. Nearly all over the park we were second best. Aberdeen were the better team, they had more quality, they played us off the park at times. We were poor, Aberdeen were very good.
"We didn't deserve to go one up, simple as that. It's a good ball in for the goal and a good finish. Big Lons (Lonsana Doumbouya) was good, he was probably our only decent performance. Everyone else was second best.
"It's one of our poorest performances of the season. We lacked belief which was strange.
"Greg Tansey and Liam Polworth, even if things aren't going well for us, will keep the ball well. But if I'm doing my job right and having players who can come in like for like, then I shouldn't be looking for them excuses and I'm not looking for them excuses.
"I've got to take some of the blame. Overall we weren't good enough today, including me."
Aberdeen manager Derek McInnes: "It was a poor goal to lose but the response was absolutely brilliant. It was three good goals from us and I thought we had some top performances, and we're in good nick now going into the Cup final.
"We've got eight games in December, almost a quarter of our season. It's mad. But when the fixtures are done at the end of that period we'll start to have an idea of where teams are.
"We're looking forward to the Cup final. I think we're past the stage of just going there and being happy to take part in a final. We're going there to enjoy it to the full and we can only do that by winning it. Celtic are a tough nut to crack but I feel the players here are capable of getting a result.
Aberdeen midfielder Kenny McLean: "We've played well in the last couple of games so going into next week we're really excited.
"Everyone wants to take points off us because we've done so well the last couple of years.
"A lot of the boys are still here that won that final (v Inverness in 2014) and there's a lot of stuff around the stadium highlighting that day. You want your name up on that wall, that's why I'm at this club. It's a massive club, you should be winning cups and challenging in the league."
Match ends, Inverness CT 1, Aberdeen 3.
Second Half ends, Inverness CT 1, Aberdeen 3.
Corner,  Aberdeen. Conceded by Josh Meekings.
Substitution, Aberdeen. Mark Reynolds replaces Graeme Shinnie.
Ross Draper (Inverness CT) wins a free kick in the defensive half.
Foul by Kenny McLean (Aberdeen).
Attempt missed. Gary Warren (Inverness CT) header from a difficult angle on the right is just a bit too high.
Attempt saved. Carl Tremarco (Inverness CT) left footed shot from the centre of the box is saved in the bottom right corner.
Goal!  Inverness CT 1, Aberdeen 3. Kenny McLean (Aberdeen) left footed shot from the left side of the box to the bottom right corner. Assisted by Jonny Hayes.
Substitution, Inverness CT. Alex Fisher replaces Billy King.
Corner,  Inverness CT. Conceded by Kenny McLean.
Lewis Horner (Inverness CT) wins a free kick in the attacking half.
Foul by Jonny Hayes (Aberdeen).
Substitution, Inverness CT. Lewis Horner replaces Brad McKay because of an injury.
Substitution, Aberdeen. Ash Taylor replaces James Maddison.
Substitution, Aberdeen. Niall McGinn replaces Jayden Stockley.
Brad McKay (Inverness CT) wins a free kick in the attacking half.
Foul by Jonny Hayes (Aberdeen).
Substitution, Inverness CT. Jake Mulraney replaces Larnell Cole.
James Maddison (Aberdeen) hits the left post with a right footed shot from outside the box from a direct free kick.
Graeme Shinnie (Aberdeen) wins a free kick in the attacking half.
Foul by Ross Draper (Inverness CT).
James Maddison (Aberdeen) is shown the yellow card.
James Maddison (Aberdeen) has gone down, but that's a dive.
Attempt missed. Lonsana Doumbouya (Inverness CT) header from the centre of the box is just a bit too high.
Kenny McLean (Aberdeen) hits the bar with a right footed shot from the left side of the box.
Aaron Doran (Inverness CT) wins a free kick on the right wing.
Foul by Kenny McLean (Aberdeen).
Hand ball by Lonsana Doumbouya (Inverness CT).
Foul by Lonsana Doumbouya (Inverness CT).
Jayden Stockley (Aberdeen) wins a free kick on the left wing.
Ross Draper (Inverness CT) wins a free kick in the attacking half.
Foul by Andrew Considine (Aberdeen).
Iain Vigurs (Inverness CT) is shown the yellow card for a bad foul.
Foul by Iain Vigurs (Inverness CT).
Jonny Hayes (Aberdeen) wins a free kick in the defensive half.
Ross Draper (Inverness CT) wins a free kick in the attacking half.
Foul by Ryan Jack (Aberdeen).
Corner,  Aberdeen. Conceded by Owain Fon Williams.
Attempt saved. Andrew Considine (Aberdeen) header from the centre of the box is saved in the top centre of the goal.
Aberdeen came from behind to beat Inverness Caledonian Thistle for the first time in five attempts.