Goals in either half from Jairo Riedewald and Wilfried Zaha, who also notched an assist, did the damage by the Thames as Roy Hodgson’s men moved up to fifth in the table with 10 points from their opening six games.
A tally like that looks a long way off for Fulham, who have now lost five of their first six games and even at this early stage they face a real challenge to avoid a relegation fight.
Boss Scott Parker will be frustrated as his side controlled much of the game, but only had Tom Cairney’s wonder strike at the death to show for their efforts.
A disappointing afternoon was made worse in the 86th minute when substitute Aboubakar Kamara was sent off for a challenge on Eberechi Eze, with referee Graham Scott changing his decision after checking the pitchside monitor.
The start to the game would have pleased Parker as Fulham zipped the ball around nicely in the opening exchanges.
But familiar problems at the back were highlighted after only eight minutes as their defence was breached in Palace’s first attack.
After Zaha had tested Alphonse Areola with a low shot, Palace recycled the ball and Zaha played in Riedewald with a delightful reverse pass which the Dutchman made no mistake in converting.
That early setback did not knock Fulham’s confidence on the ball and they began to ask questions of Palace, with Ademola Lookman’s low shot turned on to the post by goalkeeper Vicente Guaita.
Palace attacks were rare, but when they came they spelled danger and only a glaring miss from Michy Batshuayi stopped them doubling their lead as the striker put a free header from Andros Townsend’s cross wide.
Fulham should have been level in the 26th minute.
Some neat play down the left saw Lookman played in and he drilled a low effort against the post, with Aleksandar Mitrovic somehow blazing the rebound over when he had an open goal.
That was a big moment for the Cottagers as their play deserved a goal and they struggled to create anything like as clear-cut.
They were just building up a head of steam in the second half, with Cairney having an effort saved by Guaita, when Palace hit them with a sucker-punch in the 64th minute.
Townsend fed Batshuayi down the right and his devilish low cross was slid in at the far post by Zaha.
It was the Ivorian’s fifth league goal of the season and he picked up an injury for his trouble as he collided with the post, though he was able to shake it off.
Fulham ended the game with 10 men when Kamara saw red after Scott upgraded his yellow card to a straight red after a reckless challenge on Eze.
They gave themselves hope in time added on when Cairney lashed an unstoppable 25-yard drive into the top corner, but it came too late to change the game.