Match ends, Sunderland 0, Manchester United 3.
Bottom club Sunderland's hopes of avoiding relegation suffered another setback as Manchester United eased to victory to climb to fifth in the table.
Sunderland played with 10 men for more than 45 minutes after Sebastian Larsson's controversial red card for a challenge on Ander Herrera.
Zlatan Ibrahimovic had already put United ahead with a sublime, curling 20-yard effort.
Henrikh Mkhitaryan made it 2-0 before Marcus Rashford drilled in the third.
Sunderland are 10 points from safety with just seven games left and have not scored for seven matches.
United, who move above Arsenal, are four points behind fourth-placed Manchester City with one game in hand over their neighbours.
Sunderland two weeks from relegation?
This was Sunderland's 21st league defeat in 31 games this season, while they have now gone 11 hours and 15 minutes without scoring in the top flight.
It is hard to see where another win is going to come from and the Black Cats' relegation to the Championship could be confirmed as soon as 26 April - with five games remaining.
Sunderland were not helped by an injury to Bryan Oviedo, which cut short the defender's afternoon, while Larsson's contentious straight red card for going over the top of the ball on Herrera ended any realistic chance of a win before the interval.
Larsson, who was furious with referee Craig Pawson's decision, now faces a suspension for his first Premier League dismissal in what was his 278th appearance in the competition.
Moments before the red card, Victor Anichebe had been denied by United's Argentina keeper Sergio Romero, who was starting in place of the injured David de Gea.
Jermain Defoe went close from 20 yards after the interval but the Black Cats have lost six of their last seven games and look drained of any confidence.
Shaw earns a pat from Mourinho
Jose Mourinho made five changes for his side's 50th competitive game of the season but while keeper De Gea's absence was down to injury, the United boss opted to rotate players ahead of Thursday's Europa League quarter-final first leg with Anderlecht.
Luke Shaw made a surprise return just days after Mourinho had questioned the full-back's commitment and delivered a polished performance as the Red Devils stretched their unbeaten Premier League run to 21 games.
Shaw recovered from an early booking, awarded for flying in behind on Didier Ndong, to offer width and attacking threat down the left.
In front of watching England manager Gareth Southgate, he set up a great chance for Marouane Fellaini, made captain for the day four months after being booed by his own fans.
And Shaw's lively contribution also included an attempt on goal and the pass to Mkhitaryan to make it 2-0.
It was telling when Mourinho gave the 21-year-old a deserved pat on the back when he was replaced, with United in total control, soon after Ndong accidentally stood on his ankle.
Ibrahimovic's opening goal was a delight, spinning away from Billy Jones before bending home from outside the area.
No Sunderland player had touched the ball when Mkhitaryan doubled the lead 45 seconds into the second half with a low shot, while substitute Rashford completed a fine counter-attack to slot his first league goal since 24 September.
Only days earlier, Mourinho said Rashford was suffering from a major lack of confidence caused by his lack of goals.
Man of the match - Luke Shaw (Manchester United)
Sunderland boss David Moyes: "I don't want to blame referees for my position and us losing. Today the result was helped by the referee. Manchester United were playing well but the red card was a decision that went against us.
"[Before United scored] We were hanging in the game and staying in the game and trying to do our best. We gave away a poor goal and I thought we needed to get a lot closer. When we went down to 10 men it made it a lot harder.
"We keep going. We have another home game next Saturday and we have to try and win it. We do some good things but just lack a bit of quality but it's not for the want of trying. The boys are doing everything they can.
"The hardest thing as a manager is losing and we're losing a lot. The players care and want to do well and we're not doing as well as we should be."
Manchester United manager Jose Mourinho: "We want to fight in the Premier League until it is mathematically impossible. The Premier League we cannot win, but Europa League we can.
"We had lots of players that were not here today and the most important thing after the three points was to have no more injuries.
"I took Shaw off because of the yellow card and the pressure from the crowd. It was good to protect him but was also good for him to play one hour with a good solid performance and no mistakes, so I'm really pleased for him."
'Joint-second worst run in Premier League history' - the stats
- 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.
- The Black Cats' 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.
- Zlatan Ibrahimovic scored in his 21st different match of the season for Manchester United.
- 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.
- 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).
Sunderland host West Ham United in the Premier League next Saturday (15:00 BST) by which time Manchester United will have played Thursday's Europa League quarter-final first leg against Anderlecht in Belgium (20:05 BST).
- 3OviedoSubstituted forManquilloat 39'minutes
- 6CattermoleSubstituted forBoriniat 66'minutes
- 17NdongBooked at 85mins
- 7LarssonBooked at 43mins
- 36DarmianBooked at 90mins
- 23ShawBooked at 15minsSubstituted forBlindat 61'minutes
- 27FellainiBooked at 79mins
- 22MkhitaryanSubstituted forMartialat 78'minutesBooked at 82mins
- 14LingardBooked at 64minsSubstituted forRashfordat 64'minutes
- 40Castro Pereira
- Craig Pawson
- Shots on Target
Second Half ends, Sunderland 0, Manchester United 3.
Matteo Darmian (Manchester United) is shown the yellow card for a bad foul.
Foul by Matteo Darmian (Manchester United).
Didier Ndong (Sunderland) wins a free kick in the defensive half.
Attempt saved. Zlatan Ibrahimovic (Manchester United) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Anthony Martial.
Goal! Sunderland 0, Manchester United 3. Marcus Rashford (Manchester United) right footed shot from the right side of the box to the bottom left corner. Assisted by Zlatan Ibrahimovic.
Attempt blocked. Jermain Defoe (Sunderland) left footed shot from outside the box is blocked.
Attempt missed. Jermain Defoe (Sunderland) left footed shot from the left side of the six yard box is close, but misses to the left. Assisted by Victor Anichebe.
Offside, Manchester United. Zlatan Ibrahimovic tries a through ball, but Marcus Rashford is caught offside.
Foul by Daley Blind (Manchester United).
Fabio Borini (Sunderland) wins a free kick in the defensive half.
Didier Ndong (Sunderland) is shown the yellow card for a bad foul.
Matteo Darmian (Manchester United) wins a free kick on the right wing.
Foul by Didier Ndong (Sunderland).
Attempt missed. Paul Pogba (Manchester United) right footed shot from outside the box is close, but misses to the right from a direct free kick.
Paul Pogba (Manchester United) wins a free kick in the attacking half.
Foul by Didier Ndong (Sunderland).
Anthony Martial (Manchester United) is shown the yellow card for a bad foul.
Foul by Anthony Martial (Manchester United).