Once again it was veteran Swede Zlatan Ibrahimovic who provided the inspiration for Jose Mourinho's side, scoring the opener and setting up a late goal for Marcus Rashford.
Henrikh Mkhitaryan was also on target while Sunderland had Seb Larsson sent off shortly before halftime.
Six draws in their last nine league games had eroded United's hopes of a top-four finish and victory over Sunderland was imperative if they were to stay in touch.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
They were frustrated for 30 minutes but once Ibrahimovic produced a clinical finish for his 28th goal of the season in all competitions they were untroubled.
"The result was good. We resisted the results of yesterday when Manchester City and Liverpool won, they left us in a position of 'yes' or 'no'. It was 'yes'," Mourinho, whose side moved above Arsenal and are four points behind Manchester City with a game in hand, told Sky Sport.
"We got three points and it was a solid display. It was against a team that is sad, it's normal. Against a team that is sad, if you score before then it's difficult for them to react.
"You could feel the negative feeling around the team. That is felt with a team close to relegation."
Sunderland have gone seven league games without scoring and with seven games remaining they are 10 points adrift of safety and seemingly doomed to relegation.
Manager Davis Moyes said Larsson's red card for going in on high on Ander Herrera had killed the game.
"I don't want to blame referees for my position and us losing," he said. "Today the result was helped by the referee.
"Manchester United were playing well but it was a decision that went against us."
United took the lead at a sun-drenched Stadium of Light when Ibrahimovic, receiving the ball with his back to goal, shook off his marker and buried a low 20-metre shot past Jordan Pickford.
Victor Anichebe went close to an equaliser but his close-range effort was blocked by United keeper Sergio Romero who was starting in place of the injured David de Gea.
Any Sunderland hope disappeared with Larsson's red card and 46 seconds after the break Mkhitaryan fired past Pickford.
In the 89th minute Ibrahimovic combined with substitute Rashford who beat Pickford with a cross-shot for his first league goal since September.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
