Alireza Jahanbakhsh and Alexis Mac Allister both netted second-half goals for the visitors as the Seagulls continued on from their win over Newcastle over the weekend.
This happened despite Graham Potter making 11 changes from the side who thrashed the Magpies.
Albion will now face United two games in a row, in the Premier League on Saturday and EFL Cup next week.
Speaking about his team selection, Potter said: "They've earned that right.
"They played well, they've shown character, personality and quality and I'm delighted with them.
"We go into a game on Saturday, that's where our focus is. We'll see how that goes and try to prepare as well as we can and put on a good performance against a side that finished in the Champions League places.
"It's exciting, whether we play Saturday-Tuesday or Saturday-Wednesday, we'll look forward to that first game and then see what happens."