Zlatan Ibrahimovic put United 1-0 up on 30 minutes with a fine turn and low shot on the edge of the box, before Larsson was harshly sent off by Craig Pawson for a high tackle on Ander Herrera.
Just 45 seconds after the restart, United were 2-0 up through Henrikh Mkhitaryan, who found the bottom left corner from 15 yards with his left foot as Sunderland stood off.
Substitute Marcus Rashford added a third with a minute remaining, finishing well into the bottom corner from inside the area after Ibrahimovic's assist.