Brighton moved above Leeds in the Championship after Alan Navarro's injury-time winner maintained the Seagulls' unbeaten record in 2012.
Craig Mackail-Smith gave the visitors the lead from Vicente Rodriguez's cross with 13 minutes to go.
But Luciano Becchio headed the home side level two minutes later.
Navarro's deflected low drive clinched the three points for the away side, condemning Neil Redfearn to his first defeat in temporary charge of Leeds.
Redfearn's side had looked to have done enough to earn a point, but the final whistle signalled an angry response from the home fans, who held a pre-match protest march against chairman Ken Bates.
The hosts should have been ahead inside four minutes - Becchio's header grazing the post after Snodgrass had turned inside Joe Mattock.
And they had a penalty claim turned down soon after when Smith's cross from the right fell to Ross McCormack, who teed up a shot before appearing to be clattered to the ground by Adam El-Abd.
Brighton enjoyed a spell of pressure before half-time, and they almost went ahead after the break when Andrew Lonergan produced a fine one-handed save to keep out an Ashley Barnes shot.
Leeds enjoyed most of the possession but they fell behind when Mackail-Smith stole a yard in the area to notch his eighth goal of the season.
Becchio peeled off his marker at the front post to level with 11 minutes remaining, but there was still more drama to come, Liam Bridcutt winning the ball to give Navarro the chance to seal victory.
Leeds temporary manager Neil Redfearn:
"Conceding two so late is a trait which has run through this season and you can understand why it's been a problem.
"What they [the players] don't realise is, this is a fantastic club and a fantastic way to earn a living. I need to instil that in them - the problems that have been there in the past are there to see.
"It's a lack of professionalism and that's something that has run through for a while."
Brighton manager Gus Poyet (on speculation linking him with Leeds):
"I am lucky at the moment. It's a good time to be at Brighton, I make a lot of decisions.
"I say there is no chance [of wanting to leave], but it is difficult to say when the place [Leeds] is so spectacular for me.
"It would be great. I would love, in the future, to manage Leeds. I would love to come back, but at the moment the timing is not quite right. For those who want me back, I am sorry."