Eric Bailly put United in front with his first goal for the club late in the first half, during which the home side had defended resolutely.
It was not until the final 10 minutes that the visitors gave the scoreline its convincing gloss, with Romelu Lukaku, Paul Pogba and Anthony Martial all scoring in the space of four minutes.
The result follows a 4-0 victory over West Ham on the opening weekend, while for Swansea the creativity of Gylfi Sigurdsson was sorely missed.
Sigurdsson – provider of nine goals and 13 assists in the league last season – left for Everton on Wednesday in a deal worth a reported £45million following drawn-out negotiations between the two clubs.
The Iceland international had sat out Swansea’s season-opening goalless draw with Southampton last weekend, in which the Welsh club attempted just four shots on goal, and their attacking threat was limited once more on Saturday.
Jordan Ayew clipped the crossbar early on but that was one of only six attempts by Swansea – one of those on target.