Ole Gunnar Solskjaer made 10 changes to the United team that started at the weekend, with Victor Lindelof the only player to keep his place, and although United struggled for fluency they were too strong for a second-string Brighton side.
United had the first quality chance of the match in the 18th minute, but Odion Ighalo missed from a tight angle after rounding the keeper following a nice team move from the visiting side.
The teams emerged from the dressing room to more torrential rains, with Henderson again keeping his team in the lead with an excellent reaction save from Leandro Trossard's close-range shot midway through the second half.
Soon after, Mata produced a composed finish from Donny van de Beek's clever flick to double Man United's lead and register his 50th career goal since joining the Old Trafford side.
Paul Pogba, who'd come off the bench in the second half, added further gloss to the scoreline when his free kick from the left edge of the area clipped the wall and found the back of the net at the near post for a three-goal lead.
Solskjaer's team will now await the results of Thursday's Carabao Cup quarterfinal draw to see who they will face in the last eight.