Danny Welbeck opened the scoring for Albion in the 84th minute before Said Benrahma netted for the Hammers just three minutes later.
The result leaves a serious dent in the Hammers’ hopes of securing Champions League qualification this season, but manager David Moyes still found time to praise the Seagulls in his post-match press conference.
He said: "I thought we played very well for long periods in the game, especially in the first-half.
"I felt Brighton improved in the second-half.
"We didn't do enough in the final third. Our decision making was poor and there was not enough quality in the pass.
"We gave away a really bad goal. We can't keep giving the opposition a goal.
"We've had games where we've gone three or four up and tonight could have been another one if we had clinical finishing.
"All credit to Brighton. I think they are a good side."
Next up for Brighton is a clash against newly-crowned champions Manchester City at the Amex Stadium.
For the first time in months, Albion will be able to welcome a limited number of supporters back to the ground after the government eased Coronavirus restrictions on Monday.
The Seagulls were beaten 1-0 when the two sides last played each other in the league, with Phil Foden bagging the vital goal.
We’ve gathered the best of today’s Premier League transfer speculation below...

5. Toon want Roberts
Newcastle United are keeping a close eye on Leeds United forward Tyler Roberts ahead of the summer window. (Daily Mail) (Photo by Michael Regan/Getty Images) Photo: Michael Regan

6. City ready Mendes bid
Manchester City are preparing to bid £52m for Sporting Lisbon's Nuno Mendes. (Daily Mail) (Photo by Jonathan Moscrop/Getty Images) Photo: Jonathan Moscrop

7. Alderweireld wanted in Belgium
Tottenham defender Toby Alderweireld is a dream signing for Club Brugge this summer but is delaying a decision on his future. (Voetbal 24) (Photo by Clive Brunskill/Getty Images) Photo: Clive Brunskill

8. Toffees ask about Diaby
Everton have expressed their interest in Bayer Leverkusen star Moussa Diaby ahead of the summer transfer window. (Foot Mercato) (Photo by Friedemann Vogel - Pool/Getty Images) Photo: Pool

