In the 74th minute, Liverpool regained the lead thanks to Curtis Jones.
Fabio Carvalho found the back of the net from 3 yards after seven minutes of injury time, even though the referee had signalled for five.
Liverpool piled on the pressure from the blast of the whistle but Palace who lost their season’s opener to Arsenal remained resilient.
Liverpool now progress to yet another cup final this season having already won the League Cup earlier in the year and booked a place at Wembley for the FA Cup final.
Liverpool on Tuesday slipped to a shock defeat against Inter Milan at Anfield but managed to seal their place into the Champions League quarterfinals.
