The visitors were able to welcome striker Jean-Philippe Mateta back into the starting XI for the first time since his horror injury in the previous round, but his impact was limited by a dominant start from Fulham.
Opposite number Rodrigo Muniz could have opened the scoring inside two minutes after bullying his way through the Palace defence, but his left-footed strike was curled wide of the target.
Marco Silva’s men were in complete command, but working Dean Henderson was proving tricky, as Andreas Pereira proved when he dragged an effort wide following some great work down the left by Calvin Bassey.
After a stoppage in play at the first half’s midway point, Palace gained a foothold in the contest and finally threatened through Jefferson Lerma, whose outside-of-the-foot volley cannoned off the crossbar.
That was a sign of things to come as the Eagles broke the deadlock in some style through Eberechi Eze, who backed up his maiden England goal by dropping a shoulder to beat a man on the edge of the area before brilliantly curling into the bottom corner.
Four of his last five Palace goals have come in cup competitions, and he turned provider to double the visitors’ lead before the break with a pinpoint cross to the near post that was headed home by Ismaïla Sarr.
With no improvement evident from his side upon the restart, Silva turned to his bench and introduced Emile Smith Rowe and Adama Traoré in an attempt to change the game.
The Cottagers were immediately more dynamic, with Willian forcing Henderson into a smart save before Bassey was denied by a stunning block from Sarr at point-blank range.
Those misses proved especially costly, as Palace regrouped and found the net again to put the contest to bed.
Daichi Kamada released fellow substitute Eddie Nketiah to slot past Bernd Leno, putting the seal on a comprehensive victory that books their place in the semi-final at Wembley.
Fulham’s wait for a first appearance at that stage since 2001/02 continues, while they’ve now failed to win any of the last seven H2Hs on their own turf.
Flashscore Man of the Match: Eberechi Eze (Crystal Palace)