United needed a reaction after Tuesday’s surprise exit to Sevilla in the Champions League, and manager Jose Mourinho opted to leave star names Paul Pogba and Alexis Sanchez on the bench.
Mourinho told his players to “grow up” during an extraordinary pre-match news conference but the hosts produced another tepid display on Saturday, edging out the determined Seagulls to progress.
Lukaku maintained his record of scoring in every round of this season’s FA Cup, the Belgium international powering in a header from Nemanja Matic’s perfect cross.
Brighton sporadically threatened but the visitors lacked cutting edge in attack, Jurgen Locadia missing a handful of chances including a fine opportunity from a deep Solly March centre.
The Red Devils had lost three of their last four FA Cup quarter-finals but Matic headed in an Ashley Young cross late on to secure victory for Mourinho as the Portuguese seeks a second FA Cup crown, having last won the tournament in 2007 when Chelsea beat United in the final.
Luke Shaw’s driving run created space down the left and Matic’s whipped cross was perfect for Lukaku to crash home a back-post header.
Beram Kayal teed up Pascal Gross in the 51st minute but the midfielder’s 20-yard strike did not curl enough to beat the post, before Romero had to be alert to gather a Locadia drive.
Romero was soon called into action again, Valencia’s poor clearing header inviting Locadia to shoot but the Argentina international was equal to the striker’s effort, diving high to his right.
Locadia was proving a handful but he should have done better with a headed chance after March beat Young and delivered a deep right-wing cross to the back post.
Hughton threw on Brighton’s top goalscorer Glenn Murray for the closing stages but Mourinho’s men sealed victory with seven minutes left, their only attempt of the second half resulting in Matic nodding home Young’s free-kick to secure a last-four berth.