Zlatan Ibrahimovic's 28th goal of the season set the visitors on course at the Stadium of Light before Henrikh Mkhitaryan doubled the lead after Sebastian Larsson's red card.
Jose Mourinho made one or two surprising choices in his starting line-up, with Luke Shaw involved despite public criticism from his manager in the past week and Sergio Romero replacing the injured David de Gea in goal.
United nonetheless controlled things from the off against a home side with just five league wins all season and took the lead after 30 minutes through a brilliant Ibrahimovic strike.
Larsson was controversially dismissed for a tackle on Ander Herrera and United made their extra advantage count early in the second half, as Mkhitaryan struck to kill the game before Marcus Rashford had the final say late on.
United are back to within four points of fourth-place Manchester City, having played a game less, and now turn their attentions to a Europa League quarter-final first leg against Anderlecht on Thursday.
David Moyes' side remain 10 points adrift of safety at the foot of the table, though, and are looking almost certain to drop into the Championship with eight games remaining.
21 - Zlatan Ibrahimovic has scored in 21 of Man Utd's 51 games in 2016-17; no other player has scored in more than 10 (Mata - 10). Crucial. pic.twitter.com/yuWqlQX2wj— OptaJoe (@OptaJoe) April 9, 2017
Jesse Lingard, fresh from signing a new contract worth a reported £100,000 a week, tested Jordan Pickford with an unchallenged strike from 20 yards as United dominated the opening exchanges.
The visitors seemed happy to play at a pedestrian pace and Sunderland began to grow in confidence, with Bryan Oviedo and Lee Cattermole both shooting straight at Romero from outside the area.
A good run and shot from Lingard forced Pickford into a strong one-handed save but the young goalkeeper was helpless when Ibrahimovic suddenly came to life on the half-hour mark.
Collecting Herrera's pass on the edge of the area, he twisted into space before blasting a low strike across goal and into the bottom-right corner.
Romero made a fine block to prevent Victor Anichebe equalising but matters went from bad to worse for Sunderland two minutes before the interval, with Larsson shown a straight red card for a lunging challenge that caught Ander Herrera on the shin.
Larsson remonstrated furiously with referee Craig Pawson and the fourth official and Sunderland appeared to still be thinking about the controversial decision when United doubled their lead a minute after the break.
The visitors worked possession forward from kick-off until Mkhitaryan collected Shaw's pass, strode into the penalty area from the left and fired low across goal and into the bottom corner, all before any Sunderland player had touched the ball.
45 - Mkhitaryan's goal was scored just 45 seconds in to the second half & before any Sunderland player touched the ball in the half. Rapid.— OptaJoe (@OptaJoe) April 9, 2017
Paul Pogba volleyed over from close range after good work from Ibrahimovic as Mourinho began to make some changes to his side, including Daley Blind for Shaw, who got what looked to be an encouraging embrace from his manager as he left the pitch.
Substitute Rashford added gloss to the scoreline in the 89th minute with his first league goal since September, collecting Ibrahimovic's throughball before drilling low across Pickford from 12 yards, as United inflicted further misery on their former boss.
Key Opta stats:
- Zlatan Ibrahimovic scored in his 21st different match of the season for Manchester United. The Red Devils have played 51 different games, so he's scored in 41 per cent of those.
- Ibrahimovic has now scored 10 away goals in the Premier League this season; only Sergio Aguero (11) and Alexis Sanchez (12) have more on the road.
- Seb Larsson's red card was his first in his Premier League career, in what was his 278th appearance in the competition.
- Sunderland have averaged a red card every 887 minutes in Premier League history – only three teams have a worse ratio than this: Hull (720 mins), Blackburn (824 mins) and Barnsley (855).
- Manchester United's Premier League unbeaten run now stands at 21 matches (W11 D10 L0) – the joint 10th longest unbeaten run in the history of the competition.
- Sunderland have now failed to score in seven successive Premier League games – the joint-second worst run in Premier League history. Crystal Palace hold the record with nine games (1994-95), with Derby (2007-08) and Ipswich (1994-95) also going seven games without scoring.
- Sunderland's run without scoring in the Premier League now stands at 675 minutes. In that time they have attempted 79 shots in total without netting any of them.