After a string of cup upsets on Saturday, the holders made the perfect start at the Amex as Theo Walcott finished from Calum Chambers’ cross with just 89 seconds on the clock.
It got even better for a dominant Arsenal in the 24th minute as Mesut Ozil converted from Tomas Rosicky’s through ball.
The home side offered almost nothing going forward in a disappointing first-half display but they gave themselves a lifeline shortly after the break when Chris O’Grady fired into the bottom corner.
Rosicky, though, restored Arsenal’s two-goal lead when he scored with a superb volley from the edge of the box.
Sam Baldock set up a nervy finish when he coolly chipped over Wojciech Szczesny but the Seagulls could not snatch a late equaliser as Arsenal advanced into the fifth round.
The Gunners are the highest-ranked team guaranteed of a place in the next round and got off to the ideal start against their Championship opponents as they took the lead inside two minutes.
Chambers got away too easily down the right wing and crossed for Walcott, who was given too much time to turn and fire a shot past David Stockdale.
The goal was to prove a sign of things to come as Brighton gave the visitors too much time on the ball and gave it away too cheaply when they had it themselves.
Fresh off their impressive victory at Manchester City last weekend, Arsenal looked full of confidence and threatened almost every time they went forward.
They deservedly doubled their advantage in the 24th minute when the Brighton defence didn’t come out to close down the brilliant Rosicky and he threaded a ball through for Ozil to finish.
Brighton showed little sign that they would offer the same response as Bradford did at Chelsea on Saturday and the only chance they had in the first half was when Sam Baldock fired over the bar from a good position.
But the hosts were given a lifeline five minutes into the second half as Baldock knocked a header down for O’Grady and he fired a low shot into the corner.
The goal gave the home fans hopes of an unlikely comeback but it didn’t take Arsenal long to regain control of the contest as Rosicky showed excellent technique to volley home from the edge of the area.
Brighton, though, continued to rally and they pegged their opponents back again in the 75th minute when Danny Holla played a beautifully weighted pass through for Baldock, who lifted the ball over Szczesny and into the net.
Substitute Alexis Sanchez went close to netting a fourth for Arsenal as he hit the roof of the net with a free-kick but Brighton also had appeals for a penalty waved away after the ball hit the arm of Chambers.