The Seagulls ended a run of four games without a win thanks to strikes from Pascal Gross and Danny Welbeck, and moved themselves up to 14th in the table.
Graham Potter’s men are now 10 points clear of the relegation zone with just four games left to play, and while they could still mathematically go down, the likelihood of that happening now is slim to minimal.
Speaking after the match, the Albion boss was eager to praise his players for their efforts.
He said: "A big victory and a big performance.
"One with a lot of quality and a lot of character. Disappointed with the last one and you have to respond and the players did. Overall a fully deserved three points.
"We deserved the two-goal lead. Sometimes you don't get what you deserve.
"It was one of our best performances. You have to match Leeds for their effort and honesty and I felt we did that really well.
"There are still a lot of points to play for and we want to get more points as well."
Next up for Brighton is a clash against Wolves at Molineux.
Wanderers come up against West Brom in a Black Country derby on Monday evening, and will be hoping to significantly improve on their 4-0 defeat to Burnley last weekend.
We’ve gathered the best of today’s Premier League transfer rumours involving Brighton and the rest of their top flight rivals below...