The Daggers, who took the lead after just 24 seconds through John Akinde, scored twice at the start of the second half before the Seagulls sparked fans' celebration by storming back to record their 12th successive home win.
Brighton were stunned when Akinde gave Dagenham a shock lead with a deflected shot passed helpless keeper Casper Ankergren. Seagulls winger Craig Noone crashed a 25-yard drive against the bar before Brighton struck twice in the space of a minute.
A short corner from Elliott Bennett was fired towards goal by Adam El-Abd and stand-in-captain Inigo Calderon produced the final touch on the goalline. And Gus Poyet's side went ahead 60 seconds later through leading marksman Glenn Murray, who pounced for his 21st goal of the season after Marcos Painter crossed deep to the far post.
Dagenham made it 2-2 three minutes after the interval when Jon Nurse struck with a deflected shot, and Danny Green put the Daggers ahead for the second time three minutes later from the penalty spot after El-Abd brought down Akinde.
But midfielder Liam Bridcutt pulled Brighton back level after 57 minutes with an unstoppable 25-yard drive into the top corner, and substitute Ashley Barnes hit the winner by heading in a Bennett corner from the middle of the six-yard box.