The home side did all the attacking in the early stages, but the Brighton defence stood firm to thwart any opening in the final third.
Brighton's resilience eventually broke when the Red Devils were awarded penalty. Paul Pogba, who won the spot-kick, stepped up to put his side ahead from 12-yards out.
The visitors had a chance to pull level in the 35th minute when Glen Murray was played through on goal, but the veteran forward fired horribly wide with only David de Gea.
Brighton were made to rue that miss as United doubled their lead just before the break through an impressive individual goal from Marucs Rashford.
Seven minutes into the second half, Jesse Lingard should have extended the lead but the forward failed to hit the target from six-yards out at the far post.
Pascal Gross gave the visitors some hope with 20 minuets, as the Frenchman fired past David de Gea from close range after United failed to clear their lines.
Ole Gunnar Solskjaer then introduced Juan Mata and Romelu Lukaku as he looked restore the two-goal advantage.
However, the Red Devils were unable to add to their advantage as the encounter finished 2-1 in their favour.