Danny Welbeck returned to haunt United with a deserved opening goal for the Seagulls in the first half at Old Trafford on Sunday.
Second-placed United raised their game after the break, though, and the fit-again Rashford marked his return with a well-taken equalizer.
Greenwood, also passed fit after recovering from an injury, headed home the winner seven minutes from time to stun the Seagulls in the absence of Anthony Martial, who could be out for the season with a knee problem.
Victory for the Red Devils strengthened their grip on second place, 14 points behind leaders Manchester City with a game in hand, while Brighton is six points above the drop zone.
The Manchester United boss saw his side come from a goal down to beat Brighton at Old Trafford thanks to second-half strikes from Marcus Rashford and Mason Greenwood.
Ole Gunnar Solskjaer had to deliver a half-time rocket to fire his Manchester United side a step closer to Champions League football next season.
A storming second-half fightback means Solskjaer’s side is now ELEVEN points ahead of the fifth-placed Spurs with eight games left to play.
And with Leicester City and Chelsea both suffering weekend defeats, United’s grip on the Premier League’s second spot was strengthened by strikes from Marcus Rashford and Mason Greenwood after Danny Welbeck had given Brighton a deserved first-half lead.
Solskjaer said: “It’s a long way up (to City) but we want to consolidate second place.
“In the second half, we played some good stuff. The fireworks had to be lit at half-time.”
And match-winner Greenwood added: “Everyone was excellent in the second half – everyone was focused.
Maguire could count himself fortunate, though, after appearing to impede Welbeck in the penalty area when the scores were at one apiece.
Referee Mike Dean decided it was no penalty and VAR stood by his decision.
“I was a little surprised it was not given in real-time,” said Brighton boss Graham Potter. “And it looks like a penalty when you watch it back.”
Meanwhile, Solskjaer looks likely to be without striker Anthony Martial for the rest of the season.
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