Leonardo Ulloa's 87th-minute header won the day for Albion after El-Hadji Diouf's penalty had cancelled out Will Buckley's opener.
With what was at stake it was of little surprise that Brighton set off quickly. Just 29 seconds had gone when they mounted their first attack with Ulloa getting free on the right and crossing for Andrea Orlandi who, after slipping in unnoticed, bundled a close-range effort onto Paddy Kenny's post.
Rodolph Austin responded with a wayward free-kick and that kicked off a horror five minutes for the home side, starting with the 10th-minute opener.
Tom Lees failed to notice Buckley's looming presence as he sized up a backpass to Kenny and, in failing to do so, feathered the ball back allowing the former Rochdale man to nip in, set himself and score across the keeper's body.
If Lees was careless then Austin was reckless three minutes later, appearing to aggressively cut across the front of Ashley Barnes as the pair chased a ball. The striker collapsed to the floor and Austin was sent off.
It took until the 73rd minute for Leeds to get the equaliser they had threatened, although it brought another dose of controversy with it.
Diouf was about to hook a volley goalwards when he was dragged down by Inigo Calderon, with referee Graham Scott responding by pointing to the spot and sending off the last-man. The Spaniard had a head-to-head with the fourth official as he left the field before looking back to see Diouf convert the penalty he had won.
The drama was only just starting, though, as Diouf ignored his team-mate's congratulations to jog to the Brighton fans. An alleged hand gesture later and he was sent off on the advice of the linesman.
Brighton now had as much space as they needed and, with three minutes of regular time left, Ulloa headed in Orlandi's cross to put the lid on the afternoon.