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"There was happiness in our play," said the United boss. "There was no need to close the door.
"I felt in control, if you had a chance to look at me and my body language I think you could see that."
Having initially struggled to unlock their opponents' well-drilled defence despite taking the lead, United then opened the floodgates after 80 minutes as Romelu Lukaku confidently struck his third goal in two games for the club.
Paul Pogba added a third two minutes later with a delicately lifted finish and, shortly afterwards, substitute Anthony Martial fired in low to give United a second 4-0 win from their first two matches of the campaign.
"They were waiting with class, calm and consistency for the moment to kill the game," added the Portuguese.
"Swansea played with five in the back and they had a moment when they felt they had to change and when they did we had more space and killed the game.
"Anthony Martial is working hard. He is confident. The French language connection is there to help him a lot and get to the level we know he can be because the potential is huge."
Eric Bailly had tapped in just before half-time to give United a 1-0 lead after a frantic start to the match with both teams hitting the bar - Jordan Ayew's scooped cross for the hosts and Phil Jones' header for United.
After thrashing West Ham on the opening weekend, it had appeared this would be a sterner examination for United against an organised and defensively diligent Swansea side.
Mourinho's men seemed frustrated at times - Pogba had to be warned by referee Jon Moss after a quick succession of fouls - but after taking the lead, they seldom looked like squandering it against their spirited but limited opponents.
Mourinho has never failed to win the league title in his second season at a club - including both his spells at Chelsea. A summer of heavy spending had fuelled the belief he could do so again despite finishing last term 24 points adrift of the champions.
"The word that describes the team now is confident," said Mourinho.
"At the moment, everything is going in our favour - but it's not always motorway - you find difficult roads and roadworks."
With their team unchanged from last Sunday's drubbing of West Ham, United were quick to take control of this encounter, with Nemanja Matic and Pogba dictating the tempo from the base of midfield.
The visitors enjoyed as much as 66% of possession but initially lacked incision in the final third, which seemed to frustrate their players.
Pogba had to be warned by referee Moss after hauling Martin Olsson to the ground just a few minutes after he was booked for fouling Tom Carroll.
The France midfielder then went on to provide a powerful header which was brilliantly palmed on to the bar by Lukasz Fabianski, only for the ball to drop invitingly for Bailly to convert from close range.
United were happy to sit on that lead until the 81st minute when Henrikh Mkhitaryan found Lukaku unmarked in the box, and the Belgian swept in with his first real opportunity of the game.
Mourinho's side cut loose from that point, Pogba clipping the ball smartly over Fabianski and Martial finishing off a swift counter-attack to produce a scoreline which arguably flattered the visitors, as impressive as they were.
Having held on for a goalless draw at Southampton a week earlier, this was Swansea's first game since selling Gylfi Sigurdsson - pivotal in their escape from relegation last season - to Everton for £45m.
The Iceland midfielder's peach of a free-kick at Old Trafford in April was his third goal in three visits to United's home, so Mourinho and his players might have been glad to face a Swans side shorn of the influential playmaker.
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Although the Swans defended stubbornly for long periods, they offered precious little going forward.
Strikers Ayew and Tammy Abraham worked relentlessly to pressurise United's defenders, but neither had a clear scoring opportunity as their team-mates struggled to hold on to the ball.
"We were competitive for long periods of the game," said head coach Paul Clement afterwards.
"There were enough good things to say to the players - we mustn't  get our confidence affected by that.
"The second goal was even more disappointing than the first, I thought it was a gift. We missed tackles in midfield and then we were out of position at the back. They punished us and then we played to their strengths. We were 2-0 down, but a loose pass, they are so strong on the counter-attack and in the set-plays. It's a hard one to take in the end."
Clement has said he wants to use the funds from Sigurdsson's sale to sign at least two or three players and, on the evidence of their first two games of the season, he will need to spend that money wisely and quickly.
Swansea switch their attention to cup action, taking on League One MK Dons in the EFL Cup on Tuesday.
Manchester United do not enter that competition just yet - and do not have a midweek fixture. They play Leicester at Old Trafford in the Premier League at 17:30 BST on 26 August.
Match ends, Swansea City 0, Manchester United 4.
Second Half ends, Swansea City 0, Manchester United 4.
Attempt missed. Jordan Ayew (Swansea City) right footed shot from outside the box is close, but misses to the left.
Foul by Ander Herrera (Manchester United).
Tom Carroll (Swansea City) wins a free kick in the defensive half.
Foul by Anthony Martial (Manchester United).
Luciano Narsingh (Swansea City) wins a free kick in the defensive half.
Marouane Fellaini (Manchester United) wins a free kick in the defensive half.
Foul by Wayne Routledge (Swansea City).
Foul by Marouane Fellaini (Manchester United).
Jordan Ayew (Swansea City) wins a free kick in the attacking half.
Substitution, Manchester United. Ander Herrera replaces Henrikh Mkhitaryan.
Goal!  Swansea City 0, Manchester United 4. Anthony Martial (Manchester United) right footed shot from the centre of the box to the bottom right corner. Assisted by Paul Pogba following a fast break.
Substitution, Swansea City. Oliver McBurnie replaces Tammy Abraham.
Goal!  Swansea City 0, Manchester United 3. Paul Pogba (Manchester United) right footed shot from the centre of the box to the centre of the goal. Assisted by Henrikh Mkhitaryan with a through ball.
Goal!  Swansea City 0, Manchester United 2. Romelu Lukaku (Manchester United) left footed shot from the centre of the box to the bottom right corner. Assisted by Henrikh Mkhitaryan.
Nemanja Matic (Manchester United) wins a free kick in the defensive half.
Foul by Jordan Ayew (Swansea City).
Antonio Valencia (Manchester United) wins a free kick in the defensive half.
Foul by Wayne Routledge (Swansea City).
Attempt blocked. Anthony Martial (Manchester United) right footed shot from outside the box is blocked. Assisted by Romelu Lukaku.
Substitution, Manchester United. Marouane Fellaini replaces Juan Mata.
Substitution, Manchester United. Anthony Martial replaces Marcus Rashford.
Attempt missed. Paul Pogba (Manchester United) right footed shot from outside the box is close, but misses the top left corner from a direct free kick.
Leroy Fer (Swansea City) is shown the yellow card for a bad foul.
Daley Blind (Manchester United) wins a free kick in the attacking half.
Foul by Leroy Fer (Swansea City).
Daley Blind (Manchester United) wins a free kick in the defensive half.
Foul by Luciano Narsingh (Swansea City).
Corner,  Swansea City. Conceded by Nemanja Matic.
Corner,  Swansea City. Conceded by Antonio Valencia.
Attempt missed. Henrikh Mkhitaryan (Manchester United) right footed shot from outside the box misses to the right. Assisted by Marcus Rashford.
Substitution, Swansea City. Wayne Routledge replaces Kyle Bartley.
Substitution, Swansea City. Luciano Narsingh replaces Roque Mesa.
Corner,  Manchester United. Conceded by Leroy Fer.
Attempt blocked. Henrikh Mkhitaryan (Manchester United) left footed shot from outside the box is blocked. Assisted by Paul Pogba.
Henrikh Mkhitaryan (Manchester United) wins a free kick in the attacking half.
Foul by Roque Mesa (Swansea City).
Attempt missed. Tammy Abraham (Swansea City) header from the centre of the box is too high. Assisted by Tom Carroll with a cross.
Attempt missed. Leroy Fer (Swansea City) left footed shot from outside the box is high and wide to the left.
Manchester United boss Jose Mourinho said he "let the horses run freely" after a blistering three-goal burst in four second-half minutes saw his team sweep aside Swansea City to continue their impressive winning start to the Premier League season.