Fulham began the game brightly, with Rodrigo Muniz and Andreas Pereira fashioning good chances in front of a fired-up support at Craven Cottage on Saturday. Despite being under the cosh, Palace nearly took the lead when Jefferson Lerma's 25-yard volley cannoned off the bar to fire a warning shot.
Somewhat against the run of play, the deadlock was broken in the 34th minute when Eze curled in a stunning strike from the edge of the box. The England international then fizzed in a delightful cross and team-mate Ismaila Sarr got ahead of his marker to make it 2-0 four minutes later.
The deflated Cottagers took a while to find their mojo again and nearly found a way back into the game when Calvin Bassey was denied by some last-ditch defending in a goalmouth scramble.
The defensively sound Eagles, who welcomed back striker Jean-Philippe Mateta following a horror head injury, put the game to bed when substitute Eddie Nketiah beat the offside trap and fired under the body of Bernd Leno 15 minutes from time. Palace advanced to their second FA Cup semi-final in four years as they seek to lift this trophy for the first time in their long history.