Former United striker Danny Welbeck had given impressive Brighton a first half lead but Rashford pulled United level when he expertly slotted home a sharp pass from Bruno Fernandes
Greenwood sealed the victory on 83 minutes when he headed home from close range.
Brighton were fuming however as they were denied a penalty as the scores were locked at 1-1. Harry Maguire appeared to have held back Welbeck but VAR and referee Mike Dean thought otherwise.
Scroll down and click through to see how Brighton players rated
9. Leo Trossard 5/10
Quiet game for the Belgian compared to his recent performances. Replaced by Mac Allister on 64 minutes.
10. Neal Maupay 7/10
Worked tirelessly for the team and held the ball up well and linked the play. Superb cross for Welbeck's goal. Very good display from the Frenchman
11. Danny Welbeck 7/10
Has scored three goals against his former club. The focal point of the attack and finished his big chance well at the second attempt. Four goals for Welbeck this season and fans are calling for a new contract. Unlucky not to get a penalty when he appeared to be pulled back by Harry Maguire
12. Alexis Mac Allister 6/10
On for Trossard on 64 minutes but couldn't make an impact in the No 10 role