The match also witnessed three red cards in stoppage time, with Milan being reduced to nine men as tensions flared
The scoreline matched their opening-day destruction of West Ham United after Romelu Lukaku, Paul Pogba and substitute Anthony Martial scored within four minutes to add to Eric Bailly's first-half opener, his first goal for the club.
Lukaku began the late rout with a neat finish on 80 minutes for his third goal in two games before Pogba surged forward to dink the ball past Lukasz Fabianski and Martial completed the rout.
Despite raucous home support, Swansea seldom threatened in the absence of the departed Gylfi Sigurdsson the injured Fernando Llorente, always struggling to deal with United's power and pace.