Juan Fanilia-Castilo put Chelsea ahead on 10 minutes with a low strike at the Leigh Sports Village.
The Blues doubled their advantage four minutes after the break through Kylian Hazard's close-range finish, before Reece James added a superb third.
The fourth goal came 12 minutes before the end, as Harvey St Clair curled a shot beyond Kieran O'Hara.
Chelsea's third win in four matches, and their first at United in four years, lifted them to sixth on 23 points.
United, winless in eight, remain bottom with 12 points, five off safety.
Man Utd: 27 Feb v Villarreal (H) PL Int Cup
Chelsea: 2 Mar v Arsenal (A) PL2