Bryan Mbeumo's brace kept Brentford's European chances alive as Brighton, playing with ten men, lost 4-2 at the Gtech Community Stadium.
A first home Premier League win in four months puts Thomas Frank's side in the running for a top eight finish, while the confidence with which they overcame another European title challenger suggests they can keep the fight going in the final weeks of the season.
Although they remain two points behind Brighton, Brentford produced the best football in west London, opening the scoring early on when Mbeumo broke through Fabian Hurzeler's defence to score.
Danny Welbeck equalised late in the first half but Mbeumo restored the lead just after the break and then Yoane Wissa added a third with a deflected shot.
Joao Pedro was sent off inconsiderately for a challenge on Nathan Collins in the 61st minute and then Kaoru Mitoma's goal gave the visitors hope, but Christian Norgaard's final header ended those hopes.
The match ended after more than 20 minutes of second-half injury time with the disturbing sight of Brighton defender Jean-Paul van Hekke being carried off the pitch on a stretcher with a neck brace after a collision with Yunus Konak.
The hosts took the lead in the ninth minute. Vissa was denied a goal by Bart Verbruggen's outstretched leg, but the Brighton goalkeeper was powerless to stop Mbeumo's shot.
Brentford's top scorer paused his run to keep the ball in play from Keane Lewis-Potter's pass before breaking between the Brighton centre-backs and confidently firing the ball into the bottom corner.
The first half of the match seemed to be drawing to a close, but suddenly the game changed.
In the final attack before the break, Mats Wiffer flicked the ball over and Welbeck, unmarked six yards from goal, cleverly angled the ball and headed it past the stranded Mark Flecken.
However humiliated Brentford were by Brighton's ambush, they were looking to regain the lead three minutes into the second half.
It all started with a poor shot from Verbruggen that sent the ball straight back to Vissa in the right channel. He passed it to Mbeumo, who opened up his body and fired a superb left-footed shot into the far corner.
Wissa's contribution deserved a goal, and it came 10 minutes later. This time Mbeumo was the facilitator, passing into the centre to meet his teammate's run, and Wissa's shot bounced off Van Hecke.
The start of the second half was disastrous for Brighton and things were getting worse.
As Verbruggen's shot hung in the air, Pedro got into a fight with Collins and in a fit of anger punched the Brentford defender in the face. VAR recorded Pedro's violent behaviour and he was sent off, leaving Brighton playing with ten men for half an hour.
Mitoma came off the bench to slot a neat goal into the corner to set up a tense finish, but Norgaard's stoppage-time header ended the visitors' hopes.
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