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
5. Pascal Gross 6/10
Played on the right and his delivery from a first half half freekick so nearly saw Dunk head home a second. Faded in the second half as United's dominated possession
6. Yves Bissouma 6/10
Bissouma Injured his arm in the first half after colliding with Cavani. Played on and provided a solid defensive midfield base. Very disciplined and drove forward when he could
7. Adam Lallana 7/10
Looked the best midfielder on the pitch in the first half and outshone Pogba and Fernandes. Was pushed back after the break and struggled to have the same influence
8. Jakub Moder 6/10
Left wing back is far from his natural position but he did a good job for the team once again. A very athletic and physical player and seems to be settling in nicely to the Premier League