Manchester City will face Liverpool or Nottingham Forest 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.
Championship side Nottingham Forest and Liverpool play the last quarter-final at 18:00 GMT.
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.
The semi-final ties will both be held at Wembley on the weekend of 16 and 17 April.