The Gunners started quickly, and almost went ahead inside two minutes, as Gabriel Magalhães headed Martin Ødegaard’s free-kick just wide.
Julio Enciso squandered a decent chance for Brighton on the counter, blazing over in space, but Arsenal largely dictated early proceedings. Bukayo Saka curled wide on his return to the team after cutting inside, before setting up for Gabriel Jesus to fire towards goal, only for the Brazilian to be denied well by Bart Verbruggen.
The same combination were involved for Arsenal’s opener, as Jesus was tripped by Tariq Lamptey in the box, and Saka cooly slotted the resulting penalty into the bottom corner for his 14th league goal this season.
The visitors preserved their advantage before half-time thanks to a great acrobatic save from David Raya to deny Enciso from distance, rounding off an engrossing first period.
The Paraguayan was Brighton’s biggest threat, and he forced Raya into another save inside the first minute of the second half.
However, Arsenal grabbed a foothold in the game as Jesus headed Kai Havertz’s delightfully chipped cross wide at the back post, before the latter tapped home ex-Chelsea team-mate Jorginho’s pass to double the Gunners’ advantage.
Ex-Brighton star Leandro Trossard came off the bench to boos from the home crowd, and almost silenced them when his low shot was tipped past the post by Verbruggen.
He took his next chance though, chipping over Verbruggen after being put through by Havertz, capping off an impressive away performance.
Arsenal also kept a fifth consecutive clean sheet on their Premier League travels, while ending Brighton's 12-match unbeaten run on their own turf in this competition.
Mikel Arteta's men, at least temporarily, resume control of the title race, leaving Brighton five points adrift of the top-seven after a third outing in a row without victory.
Flashscore Man of the Match: Kai Havertz (Arsenal)
