Their poor run looked like continuing as Arsenal took the lead after seven minutes, Pierre-Emerick Aubameyang producing a fine side-foot finish wide in the box for his 13th league goal of the season.
However, the Gunners have only kept three clean sheets in 19 league games and were pegged back just after the half hour mark.
A long ball up the field came off the head of Stephan Lichtsteiner and fell to Jurgen Locadia who had sprinted up the field and did well to poke it past Arsenal goalkeeper Bernd Leno.
Brighton midfielder Davy Propper headed just wide shortly after halftime, while Solly March later got on the end of another long ball but his attempted lob went well over the bar.
Arsenal pressed for a late winner in stoppage time but were unable to break forward in enough numbers to breach Brighton's steadfast defence.
Unai Emery's side climbed into the top four, albeit briefly as fifth placed Chelsea, behind by only one point, take on Watford later on Wednesday.