Lukaku's 37th minute header highlighted a fairly comfortable first half for United, who were aiming to avoid exiting at the quarter-finals stage for a fourth time in five years.
Nemanja Matic scored a header of his own in 83rd minute to confirm the 12-time winners' progression after Brighton found themselves on the front foot for most of the second half.
Winter wonderland in Spring at Old Trafford
United got the first FA Cup meeting between two sides since January 1993 underway inside a scenic Old Trafford playing host to not just a football match, but what is being touted 'The Beast From The East II.'
Ryan Giggs scored the only goal in a 1-0 win on that occasion and United were hoping for a similar outcome today as they looked to bounce back from their shock European exit earlier in the week.
Antonio Valencia provided the hosts' first opening as he charged down the right flank and clipped a cross towards Lukaku from the by-line, but the Belgian no. 9 could only direct his scuffed header wide.
Brighton were carrying a threat on the break and right-back Ezequiel Schelotto was finding joy in expressing his roots as a winger up and down the right against the recalled Luke Shaw.
Lukaku heads in crucial opening goal
Slick Juan Mata and Anthony Martial link-up inside the box led to Mata having his shot deflected wide for a corner, controversially as it looked to have come off Lukaku last, after half an hour.
That corner caused a scramble around the front post before the ball eventually fell to the feet of Chris Smalling whose prodded goal-bound effort from close range was finely averted by Tim Krul.
Lewis Dunk should have given Brighton the lead minutes later, losing marker Scott McTominay from a corner and forcing Sergio Romero into a diving save at a nice height with his free header.
It was in the 37th minute when the big man stepped up, again, on the big occasion when his team needed him most as Lukaku put United 1-0 ahead with his 25th goal of the season.
Shaw bombarded down the left before dragging the ball back for Matic, whose rapid first-time cross was perfect and bounced off the head of Lukaku at the back post to lift the roof off Old Trafford.
The Belgian's opener prompted the vocal home faithful in the East-South quadrant of the stadium to ring out the Wembley chants, which is where the Red Devils were to head if things stayed the same.
Strong second half start from Seagulls
Jose Mourinho didn't look too impressed with Shaw throughout the first period and replaced with him Ashley Young, who he seems to trust more defensively, before the restart.
Although United were pinning the visitors inside their own half at the start of the second half, it was The Seagulls who were threatening to bag an equaliser in the opening 15 minutes.
First it was Pascal Gross whose curling effort from range after Beram Kayal's crisp lay-off had Romero beaten and whistled narrowly wide before Jurgen Locadia forced the Argentinian into a save just after.
Brighton's January signing was close to striking gold again before the hour mark, pulling the trigger from 20 yards out to which Romero had to respond with an acrobatic, leaping stop - clear warning signs.
With the away side growing into the game, in form frontman Glenn Murray ordered to warm up was probably not the first thing Mourinho wanted to see on the touchline with his men under pressure.
Locadia went close again after 67 minutes as Solly March convincingly beat Young on the right to then swing in a cross towards the Dutchman, who headed just over the crossbar from seven yards.
Matic calms nerves and seals progression
Another tricky winger was exactly what the in-demand defence in red would have been dreading but Chris Hughton played the Jose Izquierdo card with 20 minutes left, at the expense of March.
Marcus Rashford was then brought into the action for Mata in an attempt to keep tabs on the speed of Schelotto and Izquierdo before Murray was introduced on 76 minutes in a straight swap with Ulloa.
The 75,000 home fans in attendance were all allowed to let off a huge sigh of relief with seven minutes on the clock though as Matic headed past Krul to secure United's place in the final four.
Young curled in a delightful free-kick from deep on the left which dipped over the cluster of bodies inside the box and the unmarked Serbian towered to power his header into the net.
That was the last action of the match and it was a job done efficiently, not comfortably, by Jose Mourinho's Manchester United, who will be present in the semi-final draw ahead of the international break.