The Seagulls were in action two nights ago against Liverpool in the Carling Cup and, despite manager Gus Poyet making five changes to his staring line-up, they looked weary as Leeds raced into a two-goal lead courtesy of first-half strikes from Andy Keogh and Ross McCormack.
But a magnificent piece of individual skill from Craig Mackail-Smith reduced the arrears moments after the interval and the Scotland international then won the penalty from which Ashley Barnes netted his seventh goal of the season.
Barnes turned provider as Mackail-Smith finished from close range with six minutes to play, but McCormack intervened to check a remarkable Brighton comeback.
In the third minute, some slack marking from Danny Pugh - making his second debut for Leeds following his move from Stoke this week - might have given Brighton the lead.
From Craig Noone's corner Inigo Calderon escaped Pugh's attentions to head down for Barnes to thrash over.
But Leeds were soon into their stride, retaining possession with authority, and after Robert Snodgrass and Adam Clayton went close the latter had a hand in the opening goal in the 18th minute.
Full-back Aidy White raided down the left flank and cut back to Keogh who found Clayton on the edge of the area.
The midfielder's shot was blocked but ricocheted into Keogh's path, who slotted home his first Leeds goal with Seagulls goalkeeper Casper Ankergren stranded.
It was two six minutes later when McCormack turned to unleash a superb left-foot drive into the bottom corner from 25 yards for his eighth of the season.
Some more poor set-piece marking threatened to derail Leeds' successful half as Barnes touched towards goal but Whites keeper Andy Lonergan thwarted Mackail-Smith when the striker attempted to bundle home.
Less than two minutes after half-time Brighton were back in the contest.
Mackail-Smith collected Barnes' pass from the right and produced a sublime drag back and turn to leave the Leeds defence standing before coolly stroking into the bottom corner.
Leeds were now the team under pressure and Leigh Bromby was the man to buckle, inexplicably scything down Mackail-Smith in the box with an hour played.
Barnes netted from the spot in the 2-1 defeat to Liverpool and he was again was on hand complete the formalities from 12 yards.
Midweek exertions appeared to have caught up with both sides as the game reached its conclusion, but late drama followed in abundance.
First Calderon and Barnes combined effectively down the Leeds left to leave Mackail-Smith with a simple finish.
Simon Grayson's men were staring down the barrel of a third defeat in four away games this term, but when McCormack flicked on a long punt from Lonergan he continued his run to slam home from Jonathan Howson's cutback.
