Albion took the lead through Solly March after 14 minutes but Leeds levelled just eight minutes later through Liam Cooper.
Both sides hit the woodwork in the second period, before Zamora netted the late winner, which was his first Brighton goal in 4,549 days.
Albion boss Chris Hughton said: “We knew Leeds would be up for it and the pleasing aspect was that at a time where most probably thought it would peter out into a draw, but we showed enough determination and will to go and win the game.
“It is testament to the group of lads for wanting to go on and win the game, and in those situations and positions Bobby has that type of quality.
“We know Bobby is not the same player that he was and that he is a different type of player to what he was ten years ago, but we know what he can give us.”
Since the match, Leeds have sacked head coach Uwe Rosler after just 12 games in charge.
Click on the video above to watch Phil Hay’s video verdict of the game.
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