Marc Guehi headed the decisive goal for Palace in the closing minutes at Craven Cottage as Oliver Glasner’s side made it four victories from their last six league games.
The England defender’s late winner lifted the Eagles above Chelsea and Everton into the Champions League qualification places.
For so long one of English football’s also-rans, Palace are enjoying a golden period including last season’s shock FA Cup final victory over Manchester City and a Community Shield win against Liverpool at the start of this term.
The south Londoners are also on track to advance from the Uefa Conference League group phase, but they might have far more illustrious European opponents next season if they can keep their unexpected top four challenge on course.
Palace took the lead in the 20th minute when Adam Wharton’s pass picked out Eddie Nketiah and the forward drilled a predatory strike past Bernd Leno.
Harry Wilson equalised for Fulham in eye-catching style with a sublime strike using the outside of his foot to bend the ball past Palace goalkeeper Dean Henderson in the 38th minute.
Emile Smith Rowe thought he had put Fulham ahead but his close-range finish was disallowed for a tight offside against Samuel Chukwueze after a VAR check.
Palace took advantage of that escape to snatch an 87th-minute winner as Guehi met a corner with a thumping header past Leno.
At the Amex Stadium, West Ham were moments away from escaping the bottom three thanks to Jarrod Bowen’s second-half strike.
But Georginio Rutter grabbed Brighton’s leveller in stoppage-time to leave West Ham stuck in 18th place.
The third-from-bottom Hammers are two points behind fourth-from-bottom Nottingham Forest in the fight for survival.
Conceding so late was a painful blow for West Ham but after holding Manchester United to a 1-1 draw at Old Trafford on Thursday, West Ham’s battling display was further evidence of their improvement since Nuno Espirito Santo replaced the sacked Graham Potter in September.
West Ham have lost just one of their last six league matches to revive their survival hopes.
Brighton blew a two-goal lead in a 4-3 defeat against Aston Villa in midweek, surrendering their 10-match unbeaten run at home in the process. (AFP)