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."

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However, he was withdrawn just before Greenwood bagged his second of the game, with Cavani adding gloss to the scoreline for United's fifth successive league victory.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."

Burnley had been undefeated in their four previous visits to Old Trafford and they started well on Sunday, with only an offside flag denying Chris Wood after he beat Dean Henderson to Matt Lowton's hopeful ball forward.

They fell behind when Rashford ran down the left hand channel and squared to Bruno Fernandes, who allowed the ball to drift through his legs for an unmarked Greenwood to slam a first-time shot beyond Bailey Peacock-Farrell.

Tarkowski rose above Harry Maguire to level but Greenwood restored United's lead late on, with his shot taking a cruel deviation off Jack Cork, wrongfooting Peacock-Farrell, who was beaten again by Cavani in time added-on.

Burnley boss Sean Dyche said: "Overall I was pleased. At 1-1, I think we're seeing the game out well and we might have a chance of nicking one because it looked like that type of game. But they get one out the blue.

"You're scratching your head at that stage because I thought we were handling the game very well. You don't want to cry too much, over the season you need your scratches of your luck."

A third successive defeat means 17th-placed Burnley sit six points above the relegation zone following Fulham's draw at Arsenal earlier on Sunday.

Dyche added: "The mentality in training is very good, the performance was very good, we've got to keep showing that in these remaining games."