Sunderland suffered an early blow in the match when Connor Wickham went off with what looked to be a serious ankle injury.
United gradually took control of the match and were ahead when former United defender Wes Brown deflected a Nani corner into his own net during first-half injury time.
Sunderland thought they had a chance to get back into the match when the linesman flagged for a handball against Phil Jones in the Manchester United penalty area.
However, referee Lee Mason spotted that it was Ji Dong-Won's hand that touched the ball and overruled his assistant.
United continued to attack and Keiren Westwood kept Sunderland in the match with a double save late on.
The Reds comfortably saw out the match and the result means that Steve Bruce still hasn't beaten Manchester United during his career as a manager.
Meanwhile, Sunderland are still without a win at Old Trafford since 1968.