Free-scoring United hit four for the second time in a week with a devastating burst of three goals in the last ten minutes at the Liberty Stadium.
In the Reds best league start for 110 years, Eric Bailly prodded in his first for the team on the cusp of half-time, before Romelu Lukaku, Paul Pogba and Anthony Martial all scored for the second successive match as the Reds pulled away late on.
The game was not as comfortable as the eventual scoreline suggested, with United on the back foot at times and Pogba perhaps fortunate to avoid being sent off after a clash with Martin Olsson.
The Frenchman had earlier been booked for a challenge on Tom Carroll, and a similar coming-together with Swans full-back Olsson could, on another day, have resulted in a second.
Having thrown down the gauntlet against West Ham the previous weekend, Jose named an unchanged side for the trip to United's traditional bogey team.
Jordan Ayew went close for the Swans early on when he clipped the bar, before Lukaku flashed a shot wide after a quickfire counter-attack at the other end.
Phil Jones headed off the woodwork from a Juan Mata free-kick on ten minutes, but the Reds struggled for clear cut chances against Swansea's rigid and disciplined five-man defence.
The elusive breakthrough finally arrived on the stroke of the half-time, though, when Bailly opened his account for the club.
Daley Blind's corner picked out Pogba who headed against the underside of the bar and the rebound fell to the Ivorian to poke home on the line.
Henrikh Mkhitaryan drilled a shot wide and man of the match Pogba went close with a 20-yard free-kick as United started the second half brightly.
Leroy Fer fired an effort narrowly off-target but any hopes Swansea had of pinching a point were swiftly ended by United's lethal late salvo.
Fresh from scoring twice on his Old Trafford debut, Lukaku got in on the act again when he collected Mkhitaryan's pass and rifled beyond Swans stopper Lukasz Fabianski on 80 minutes.
Just as they did against the Hammers last time out, Pogba and substitute Martial both found the net with two goals in as many minutes.
Pogba clipped home an instinctive finish after more good work from the mercurial Mkhitaryan on 82 minutes before he turned provider for compatriot Martial.
The two Frenchmen linked up again as the former found the latter - who had just come on - and he rolled the ball home from close range six minutes from time to complete another resounding win.
Two games, six points, eight scored and none conceded - United's 2017/18 campaign could hardly have started better.
Overall team performance: 8.5/10
United Faithful Man of the Match: Paul Pogba