Despite fielding a nearly full-strength side, Liverpool were undone by Marco Reich's goal in the 66th minute that booked Palace's place in the fourth round.
Skipper Steven Gerrard's goal offered Liverpool little consolation after they were beaten by workmanlike Palace, who took the lead through Dougie Freedman.
It was the Premiership team who started the brightest. Peter Crouch should have given them the lead in the fif minute but his header from Gerrard's corner struck team-mate Harry Kewell.
Kewell then blazed his shot over the bar from the edge of the box before Fernando Morientes' effort was well saved Palace keeper Julian Speroni.
On 22 minutes Speroni was again called into action when he was at full stretch to tip Gerrard's curling drive around the post.
Palace had their chances and were denied an excellent chance by a piece of poor refereeing by Phil Dowd. Mr Dowd decided to stop play for a challenge on Freedman, despite Clinton Morrison being through on goal.
Reich and Freedman also had chances before they took the lead in the 37th minute when Freedman got behind Zak Whitbread to head in Michael Hughes' cross.
Their lead lasted just three minutes when Gerrard grabbed an equaliser. The skipper marked his return from injury with a low drive from the edge of the box after Mark Hudson had failed to clear the ball.
Palace more than matched Liverpool and when Reich struck in the 66th minute it was no less than they deserved. The German midfielder struck a sweet half-volley past Scott Carson after Hughes had supplied a precise pass to the back post.