Zlatan Ibrahimovic set them on their way with a superb curling finish from Ander Herrera's pass.
A foul on Herrera resulted in a red card for Sunderland's Sebastian Larsson shortly before half-time.
Man Utd went 2-0 up soon after the break, with Henrikh Mkhitaryan slotting in after a fine team move, before Ibrahimovic teed up Marcus Rashford to fire in a late third.
The win leaves United four points behind fourth-placed Manchester City with a match in hand, while Sunderland remain bottom, 10 points adrift of safety.
Man of the match Zlatan Ibrahimovic (Man Utd)