The result left United second in the standings on 66 points from 32 games, eight behind leaders Manchester City and 10 ahead of third-placed Leicester City, who have a game in hand.
Greenwood fired United ahead in the 48th minute and after James Tarkowski headed Burnley’s equaliser two minutes later, he restored the home side’s lead with a heavily deflected shot before Edinson Cavani sealed the win.
United enjoyed a huge let off in the first minute as Burnley striker Chris Wood headed the ball into the back of the net after only 13 seconds but his effort was ruled out for a marginal offside.
Visiting goalkeeper Bailey Peacock-Farrell did well to deny Paul Pogba and Marcus Rashford in the first half before Greenwood fired the home side ahead when he capped a slick move with a clinical finish.
Tarkowski rose above Harry Maguire to head home an Ashley Westwood corner but Greenwood struck again in the 84th minute and halftime substitute Cavani put the icing on the cake for United in stoppage time after another flowing move.
Rashford injury update
Rashford was a doubt for this fixture due to the foot and ankle issues he has had in recent weeks, but he was at the heart of some of United’s best bits of play and teed up Greenwood for United’s opener.
However, he was withdrawn just before Greenwood bagged his second of the game, with Cavani adding gloss to the scoreline for United’s fifth successive league victory.
Solskjaer said: “I asked him (Rashford) how he was. Because he played so well and he felt good out there, I was trying to force 90 minutes out of him but he said that he was too sore.
“It’s just pain that comes after he’s played for 60 or 70 minutes. He lasted 80 here so that was progress. I thought he played in the second half so well. He made some great runs in the first half but we didn’t find him.”
Solskjaer pleased with fighting spirit
Solskjaer praised United’s resolve after breaking down Burnley’s resistance with two late goals.
Victory moved the Red Devils eight points behind leaders Manchester City and while Solskjaer conceded their hopes of catching their crosstown rivals is unrealistic with only six games of the season remaining, the Norwegian has not written off their hopes entirely.
He said: “I’m really proud that we never gave up and that we’ve proven so many times this season our fitness and resilience.
“We came back and scored three goals last week (in a 3-1 win at Tottenham), we’ve scored three goals in the second half here as well.
“Our fitness, confidence and belief has improved so much this season compared to last year. That’s big, big progress.
“(Catching up to City) is probably unrealistic but stranger things have happened in football and we’ve just got to do our job and see what everyone else does.”
Neville slams European Super League plans
Gary Neville is absolutely furious on Sky Sports. He claims the European Super League plans are a “criminal act” against the fans in England, and the decision is being driven by the greed of the owners.
Meanwhile, the news that Manchester United could be one of the ‘Big Six’ Premier League clubs who are set to join a breakaway European Super League.
United, Liverpool, Arsenal, Chelsea, Tottenham and Manchester City have signed up to the breakaway plan, according to reports, and will be joined by teams from Italy and Spain.
A joint statement from Uefa, the Football Associations of England, Spain and Italy, plus the Premier League, LaLiga and Serie A added they remained united in their efforts to “stop this cynical project” and were considering all “judicial and sporting (measures) in order to prevent this happening”.
So, another win for Manchester United puts them eight points behind leaders Man City – still realistically too far off to hope for the title, but we’ve seen collapses before…
GOAL! Manchester United 3-1 Burnley | Edinson Cavani, 92 mins
United just about clear their lines but then break against a tired Burnley.
Cavani to Greenwood, Bruno to Van de Beek on the left, and he tees up Cavani for a tap-in.
Burnley break, Lindelof is inexplicably beaten when he should take out his man, but Burnley can’t make the chance count…
91 mins: United play the corner short and Pogba wins a free-kick with a shout. Pogba isn’t happy with the referee.
90 mins: Bruno almost finds a third as he rounds the keeper and blasts at goal – he wants a penalty for handball, but nothing doing.
Chance for United!
It should be 3-1 as Cavani finds Greenwood, who slips in McTominay – but the Burnley keeper makes a great low stop.