Robin van Persie provided an exhibition of superb finishing with two goals and Danny Welbeck also netted a brace in an emphatic away win, while Wilfried Bony scored for Swansea.
The crucial spell came towards the end of the first half as Van Persie fired home an acrobatic opener in the 34th minute and Welbeck added a second two minutes later to put United in control at the interval.
Van Persie made it 3-0 with a spectacular strike from distance in the 72nd minute, before Swansea's club-record signing Bony pulled one goal back eight minutes from time.
United were not finished, though, and Wayne Rooney played his part after coming on as a substitute by playing in Welbeck for an exquisite chipped finish.
The confidence of winning five championships in the past seven seasons was in evidence throughout the first half as United soaked up pressure, then struck with deadly efficiency.
Swansea had already escaped from a couple of defensive lapses, as Ryan Giggs elected to try and find Welbeck when it seemed more obvious to go for goal himself, before Michel Vorm turned over Phil Jones' volley.
Even Van Persie had failed to take a decent opportunity. But when the Dutchman evaded the attentions of the home defence and was allowed to drift into space behind the centre-halves because Angel Rangel was playing him onside, there was only ever likely to be one outcome.
And Van Persie showed the class that made him a back-to-back Golden Boot winner, hooking a shot into the corner to make him the first United player to score a league goal for someone other than Ferguson since Peter Davenport.
Welbeck found the net just once in domestic combat last term, but within a minute of Van Persie's effort, he had matched that figure.
Again Swansea were architects of their own downfall as Ben Davies got sucked into a central position attempting to clear a Patrice Evra cross. That allowed Antonio Valencia to return the ball to the edge of the six-yard area, where Welbeck turned it home.
It was no surprise Swans manager Michael Laudrup sent a call out for £12million record signing Bony at the break though, the striker having missed out on a starting berth due to midweek international duties in the United States.
Rooney was introduced for Giggs shortly afterwards, a move well received by the visiting contingent, who bellowed the striker's name in their usual manner, with no hint of annoyance.
And Rooney claimed an assist for Van Persie's second, finding his strike partner with a short pass.
Williams paid the price for standing off on the edge of his own box and after Van Persie stepped round Chico Flores he applied a brutal finish from 20 yards that flew into the top corner.
Bony netted a consolation for Swansea after good work by Pablo Hernandez but the contest itself was already over, and Welbeck eclipsed last season's meagre tally in stoppage time with a wonderful chipped finish.