Manchester City will play either Liverpool or Nottingham Forest in the FA Cup semi-final at Wembley.
Crystal Palace, who beat Everton 4-0 and never won the FA Cup, will play last year’s finalists Chelsea in the London derby in another match.
Champion teams Nottingham Forest and Liverpool play in the last quarter-final at 18:00 Moscow time.
Chelsea beat Middlesbrough 2-0 on Saturday and Manchester City beat Southampton 4-1.
League Cup winners Liverpool are chasing the quad this year, while Premier League leaders City are chasing the treble.
Both semi-finals will be held at Wembley on 16 and 17 April.