Manchester City will face Liverpool in the FA Cup semi-final at Wembley.
Crystal Palace, who beat Everton 4-0 and have never won the FA Cup, play last year's beaten finalists Chelsea in a London derby in the other game.
Liverpool were made to work hard against Nottingham Forest but eventually progressed thanks to Diogo Jota's goal.
Chelsea won 2-0 at Middlesbrough on Saturday, while Manchester City picked up a 4-1 success at Southampton.
Carabao Cup winners Liverpool are chasing a quadruple this year, while Premier League leaders City are in the hunt for a Treble.