Fulham's took the lead late on in the first-half when Emile Smith Rowe scored in the bottom-right corner after he intercepted a loose pass from Maxence Lacroix near the halfway line, before the ball fell for Raul Jimenez, who played Smith Rowe through on goal in the 47th minute.
The former Arsenal man thought he had doubled the lead in the 52nd minute, but while Alex Iwobi's low cross found Smith Rowe inside the penalty area via two deflections, the goalscorer was just offside and his second strike was ruled out by the VAR.
The Eagles were reduced to 10 men when Daichi Kamada was sent off for a dangerously high tackle on Kenny Tete in the 76th minute, before Iwobi played a defence-splitting pass from the left touchline into the box towards substitute Harry Wilson, and the forward swept the ball past Dean Henderson in the 83rd minute.
The result means Palace are 17th with seven points from 11 games and head into the November international break just one point ahead of 18th-placed Wolverhampton Wanderers in the relegation zone.
Fulham started the day in ninth place and after their win the Cottagers rose to sixth place with 18 points, and they are level on points with fifth-placed Arsenal and sixth-placed Chelsea, who play the Gunners on Sunday in the Premier League.
The Cottagers were first goal was well taken, though they were fortunate that centre-back Lacroix recklessly gave up possession in the 47th minute, but perhaps goalkeeper Henderson should have done better to keep the ball out considering he made strong contact with the ball.
Fulham counter-attacked at pace following a poor Palace free kick into Bernd Leno's penalty area in the 52nd minute, and the visitors played towards an unmarked Iwobi just inside the right side of the box, but Smith Rowe was offside as he tapped home his cross in the six-yard box.
Substitute Wilson can thank Iwobi for his goal given the winger played a delightful pass from out wide on the left into the penalty area, registering his first assist of the game after initially he was denied one when Smith Rowe's second goal ruled out.
CRYSTAL PALACE VS. FULHAM HIGHLIGHTS
45+2nd min: Crystal Palace 0-1 Fulham (Emile Smith Rowe)
Lacroix plays a loose pass that Smith Rowe intercepts into the path of Jimenez, and the striker returns the ball to the Englishman, who races away through to goal and nets his side's opening goal in the first-half stoppage time.
What was Lacroix thinking?
CRYSTAL PALACE VS. FULHAM HIGHLIGHTS
76th min: Red card (Daichi Kamada)
Kamada attempts to tackle Fulham's Tete for possession of the ball in the 76th minute, but his challenge is reckless and catches the right-back at shin height, which warrants a red card.
Kamada can have no complaints.
CRYSTAL PALACE VS. FULHAM HIGHLIGHTS
83rd min: Crystal Palace 0-2 Fulham (Harry Wilson)
Iwobi picks up the ball on the left touchline some distance away from the box, but he threads a spectacular ball through Palace's defence for substitute Wilson, and the attacker strokes the ball from the left of the penalty area past Henderson.
What a pass from Iwobi!
MAN OF THE MATCH - EMILE SMITH ROWE
After struggling for game time during his Arsenal career, Smith Rowe is finally being allowed to flourish and showcase his immense talent.
The midfielder scored his side's opening goal after pouncing on an error from Lacroix, and he was unlucky that his second was ruled out by the VAR after he was adjudged to have been offside.
Smith Rowe also had six touches in the opposition penalty area, the joint most of any player on either team, and proved how threatening he can be inside the box.
CRYSTAL PALACE VS. FULHAM MATCH STATS
Possession: Crystal Palace 35%-65% Fulham
Shots: Crystal Palace 13-17 Fulham
Shots on target: Crystal Palace 5-7 Fulham
Corners: Crystal Palace 1-8 Fulham
Fouls: Crystal Palace 10-11 Fulham
BEST STATS
WHAT NEXT?
Crystal Palace next take on Aston Villa at Villa Park on November 23 in the Premier League, before facing Newcastle United at home on November 30 in the league.
As for Fulham, they are set to host Wolverhampton Wanderers in their next outing in the top flight in on November 23, before taking on Tottenham Hotspur away from home on December 1.