The forward suffered a serious head injury in the previous FA Cup round against Millwall on March 1, when he was kicked in the head by opposing goalkeeper Liam Roberts. Mateta was taken to the hospital, where he received 25 stitches as one of his ears had been torn apart.
Mateta has been absent since then, but made a surprising comeback from the start as early as Saturday.
Palace took control of the game at Craven Cottage after just over half an hour, when Eberechi Eze first scored 1–0 and then Ismaila Sarr headed in 2–0 four minutes later.
Eddie Nketiah sealed the 3–0 win in the second half.
Thus, Crystal Palace is the first team to qualify for the semifinals at Wembley.
In Saturday's other quarterfinal, Nottingham won away against Brighton. The 0–0 match was decided on penalties.
Yasin Ayari started for Brighton, but was substituted. Anthony Elanga began on the bench for Nottingham, but was brought in.
On Sunday, Preston will face Aston Villa and Manchester City will meet Bournemouth away.