Daichi Kamada’s weighted pass found Eddie Nketiah in behind the Fulham defence and his cool finish sealed the tie in front of an ecstatic travelling support.
That finished off the hosts challenge, with Nathaniel Clyne and Justin Devenny also introduced as late substitutes for the Eagles.
The remainder of the game passed mainly without incident, leaving the Palace fans to serenade the team with choruses of “Wembley again, ole, ole.”
We will find out our semi-final opponents tomorrow afternoon in draw, which follows the Preston-Aston Villa tie.
Palace: Henderson (GK), Richards, Guéhi, Lacroix, Muñoz (Clyne, 86), Mitchell, Lerma, Wharton (Kamada, 69), Eze (França, 90), Sarr (Devenny, 86), Mateta (Nketiah, 69)
Subs: Turner (GK), Chilwell, Kporha, Esse.
Fulham: Leno (GK), Castagne, Anderson, Bassey, Robinson (Sessegnon, 69), Berge, Lukić (Traoré, 62) Pereira (Smith Rowe, 62), Iwobi (Cairney, 82), Willian (Jimenez, 69), Muniz.
Subs: Benda (GK), Diop, Cuenca, Reed.