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
1. Robert Sanchez 6/10
No chance with Rashford's goal and beaten by Greenwood's scrappy winner. One risky pass in the first half when trying to play out from the back and saw Greenwood's effort hit the base of the post early on. Remained steady and confident throughout. Very acrobatic stop to close down Fernandes on the hour.
2. Ben White 7-10
On the right of a three man defence and for the most part coped well with the threat of Rashford. The United striker though took his goal well and just slotted his finish beyond White's despairing sliding tackle. White So close to clearing Greenwood's winner off the line
3. Lewis Dunk 7-10
Had a great chance in the first half when his powerful header from Gross' freekick was tipped over. Defended well and totally nullified Cavani
4. Joel Veltman 6/10
Doesn't matter where you place him on the pitch he looks comfortable. Defends well and unlucky to be on the losing side