Tresor Kandol turned from villain to hero as Leeds remained unbeaten. The former Barnet striker missed a penalty a week ago in the 1-1 home draw against Leyton Orient.
He was on hand this time to pounce on a blunder by Brighton defender Adam El-Abd 11 minutes from time.
A cross from Frazer Richardson looked harmless as it bounced towards the near post. El-Abd mis-kicked, glancing the ball back towards his own goal.
Goalkeeper Michel Kuipers was at full-stretch to keep it out one-handed, but Kandol was there to pick up the pieces and convert his sixth goal of season from close-range.
It gave Leeds a victory they scarcely deserved in front of a record crowd at Withdean.
They had to play second-fiddle to in-form Brighton for most of the match and the home side were unfortunate to see their own unbeaten run of five games come to an end.
The lively Jake Robinson forced United's Danish keeper Casper Ankergren into a fingertip deflection early on, with a rasping shot from long range.
Frenchman David Martot also should have done better in the first half with a half-volley wide from a cross by Andrew Whing.
The prolific partnership of Kandol and Jermaine Beckford was kept quiet by a Brighton defence bidding for a fifth successive clean sheet in the League, although Kandol should have done better with an early header from a David Prutton cross which finished well wide of the target.
Kuipers acrobatically foiled a right-foot volley from former Brighton winger Seb Carole, but it was the home side who continued to carry the game to Leeds in the second-half.
Ankergren had to stretch to hold a curling effort from Alex Ravel and Martot went close with a swivelling right-foot volley from a cross from Bas Savage.
Leeds showed great resilience to hold out and have now won ten times in the League and drawn the other two.