Brighton took the lead at the Emirates Stadium when Leandro Trossard turned home a low cross from Enock Mwepu to finish a good move from the visitors.
Arsenal had struggled to create chances but thought they had levelled through a close-range effort from Gabriel Martinelli, only for a lengthy VAR check to cancel out his header.
Arsenal named Granit Xhaka at left-back as they made two changes for the visit of Brighton.
The Gunners lost 3-0 at Crystal Palace on Monday night and the injured Thomas Partey was replaced by Albert Sambi Lokonga.
Nuno Tavares was hauled off at half-time at Selhurst Park and lost his place to Gabriel Martinelli as Xhaka filled in at full-back.
Brighton ended a six-game losing streak with a 0-0 draw at home to bottom club Norwich last weekend and Graham Potter's team started well.
Moisés Caicedo impressed in the Albion midfield on his debut. The Ecuador international delivered a powerful and composed first half display.
Mwepu, who has had his injury troubles this season was also an influential figure and will hope to have a strong end to the season.
His return to fitness is a timely boost following the serious ACL injury sustained by Jakub Moder against Norwich.