Robert Snodgrass caught stand-in goalkeeper Graeme Smith slightly out of position with an in-swinging left-foot shot from 20 yards in the 27th minute.
Leading scorer Jermaine Beckford notched his 13th of the season two minutes before the break from close range after Glenn Murray was dispossessed and Neil Kilkenny delivered a perfect 80-yard ball up front.
Defender Patrick Kisnorbo should have increased Leeds’ advantage shortly after the break, but put a free header wide following a free-kick by Snodgrass.
Brighton went close when striker Murray headed a Dean Cox cross wide at the near post.
Australian midfielder Kilkenny sealed Leeds’ comfortable win in the last minute by latching on to a cross from substitute David Prutton to fire home from 12 yards.