Matters got worse for Leeds when Rodolph Austin was sent off for pushing Ashley Barnes in the face, reducing Brian McDermott's side to 10 men after just 13 minutes.
The home side had late efforts to try to get an equaliser but both El-Hadji Diouf and Ross McCormack couldn't hit the target with shots from outside the penalty area.
Leonardo Ulloa almost doubled his side's lead after the break when he collected the ball from Barnes on the edge of the area and turned, but his effort went wide.
Leeds were handed a way back into the game when Diouf was brought down in the box by Inigo Calderon and they were awarded a spot kick, while the defender saw red.
Diouf stepped up and scored but while celebrating he gestured towards the away fans and was duly sent off, reducing the hosts to nine men.
Brighton upped the ante and regained the lead late in the game when Ulloa headed home from close range, nodding in Andrea Orlandi's pinpoint cross to seal the win for his side.