Eric Bailly opened the scoring in the final minute of the first half, before Romelu Lukaku, Paul Pogba and Anthony Martial all got on the scoresheet within a four-minute period during the closing stages.
The result was harsh on Swansea, who remained competitive throughout the contest, but United's extra quality in the final third eventually proved the difference and Jose Mourinho's side already boast a strong goal difference while sitting at the top of the standings.
Swansea almost took an unlikely lead in just the third minute when Jordan Ayew broke clear down the left before seeing a cross with the outside of his right foot strike the underside of David de Gea'a crossbar before being cleared.
United began to dominate possession but Mourinho's side were struggling to carve out clear-cut opportunities against their hosts, who put each player behind the ball aside from Tammy Abraham.
As the half-hour mark approached, Pogba went into the book for a cynical foul on Tom Carroll and the Frenchman was fortunate to avoid a second yellow for a late, but non-aggressive, challenge when attempting to close down a defender.
Swansea should have perhaps taken the lead with 11 minutes of the first half remaining when Kyle Bartley rose to meet a corner but he directed his header well wide of De Gea's post.
Moments later, it was Marcus Rashford's turn to waste a chance to open the scoring when a poor header from Alfie Mawson sent him clear on goal, but the pacey attacker clipped the ball straight at Lukas Fabianski.
However, in the final minute before the break, United went in front through Bailly, who tapped home from on the line after Fabianski had made a sensational save to tip Pogba's free header onto the underside of the crossbar.
United picked up where they left off after the restart but Swansea were doing a solid enough job of keeping chances few and far between, with only a long-range Rashford shot forcing a save out of Fabianski.
However, Swansea eventually showed more ambition and on the hour mark, Carroll's driven cross found the head of Abraham, who powered the ball marginally off target.
Ayew was offering a constant threat for the home side but still, Swansea were unable to build on the amount of possession they were enjoying in the final third.
Back up the other end, United won a free kick at goal around 25 yards out but Pogba's well-struck effort marginally missed the top corner with Fabianski beaten.
With 10 minutes to go, Swansea were still in the game but three goals in the space of four minutes earned United a lopsided win, a period which sends another message to their title rivals.
Lukaku got on the scoresheet for the second game running when receiving Henrik Mkhitaryan's pass and finding the bottom corner from 12 yards, before the Armenian was again the creator when setting up Pogba to direct the ball inside the near post from a similar distance.
At this stage, Swansea were wilting and United took full advantage with a fourth goal from substitute Martial, who curled the ball into the far corner after the home side's defence had allowed him to run towards goal.
The home team managed to avoided conceding a soul-destroying fifth, but United and Mourinho will be delighted with another powerful performance during the opening weeks of the new season.