In a game which lacked some of the drama from the Premier League meeting at the Amex Stadium four days earlier, the visitors progressed with a deserved 3-0 victory.
Juan Mata laid on the opener for Scott McTominay before adding the second himself with his 50th goal for the club.
Paul Pogba came off the bench to score late on as Ole Gunnar Solskjaer’s side eased into the last eight.
“It was a tight game until the second goal, or Dean Henderson’s save at 1-0 was key,” said Albion head coach Graham Potter. “Then they bring on Rashford and Pogba which made life difficult.
“The first goal is not a good one, we have to do better there, it’s as simple as that.
“We were in the game, 3-0 is a bit harsh.”
Brighton made nine changes and United 10 from their weekend clash which was won by Bruno Fernandes’ penalty awarded after the full-time whistle.
On a rain-soaked evening this was no match for that five-goal thriller as United won their third game at Brighton in three months.
Graham Potter retained Ben White and captain Lewis Dunk as the Seagulls failed to gain retribution for their painful weekend defeat.
United took the lead just before the interval, Mata picking himself up after being tripped by Dan Burn to bend in a free-kick which McTominay headed home.
Leandro Trossard hit the woodwork three times on Saturday and the second half substitute was denied again here by a fine Henderson stop after persistent play from Jayson Molumby.
Dunk then headed over when he arguably should have done better, but Brighton were not able to stage a rousing cup comeback.
Those chances were enough for Solskjaer to call for the cavalry as Pogba and Marcus Rashford were introduced from the bench with a little under 30 minutes remaining.
The tie was wrapped up shortly after as Mata finished with aplomb having been teed up beautifully by Van De Beek.
There was still time for Pogba to score just his second goal of 2020, the France midfielder seeing a free-kick take a big deflection on its way past Jason Steele.
Ole Gunnar Solskjaer said, “A great performance by Juan Mata. He was the one who got on the ball and calmed us down. He was composed. He more or less creates the first goal himself. I am never surprised when he plays like this.
“He has been around the block and knows football. He does his work and is at the back stick to shield the ball from Dan Burn at a corner in the second half.
“We needed the first 20-25 minutes to get our confidence and get on the ball. We have worked on set pieces. You keep a clean sheet and this is important for a back four.”