It was Brighton' s first Premier League victory since November as they halted a 10-game winless run in all competitions.
Maupay gave the visitors the lead in the 17th minute after good work in the penalty area from Leandro Trossard and Alexis Mac Allister.
Albion also hit the crossbar through Trossard’s deflected cross in the first and the Belgian then fired over in the second half when he had a chance to make it 2-0.
There were some excellent individual performances with Adam Webster, Ben White and Alexis Mac Allister all outstanding for Graham Potter's team.
The win moves Brighton to 16th above Burnley, who suffered a 1-0 loss against West Ham earlier.
Scroll down and click through to see how they rated
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Brighton celebrate their excellent opening goal at Elland Road
. Robert Sanchez 7/10
Calm and assured once more. Very alert and gathered crosses into the box well
. Joel Veltman 7/10
The more he plays the comfortable and better he looks. 900k was money well spent on the summer arrival from Ajax. Excellent in possession and rarely makes a mistake.
. Adam Webster 8/10
Playing the best football of his career at the moment. Defensively sound and carries the ball forward with intent - even across the terrible playing surface at Elland Road
1. Robert Sanchez 7/10
Calm and assured once more. Very alert and gathered crosses into the box well
2. Joel Veltman 7/10
The more he plays the comfortable and better he looks. 900k was money well spent on the summer arrival from Ajax. Excellent in possession and rarely makes a mistake.
3. Adam Webster 8/10
Playing the best football of his career at the moment. Defensively sound and carries the ball forward with intent - even across the terrible playing surface at Elland Road
4. Lewis Dunk 7/10
Consistent high level of performances from Dunk for the last two months. Always seemed to be in the right place against Leeds and kept Bamford pretty quiet fr the most part