Fulham's reward for knocking out holders Manchester United is a home London derby with Crystal Palace in the FA Cup quarter-finals.
Bournemouth have been drawn at home to Manchester City.
Preston, the only Championship side left in the FA Cup, are at home to Unai Emery's Aston Villa.
And Brighton will be at home to either Nottingham Forest or Ipswich, who play their fifth-round tie on Monday.
Aside from 2023 victors Manchester City, Ipswich are the most recent FA Cup winners (1978) left in it.
Fulham, Palace, Bournemouth and Brighton have never won the cup.
"It's very open now. What a chance for a team to go and win it," said ex-Manchester City and Villa defender Micah Richards on BBC One.
"All the [other] big teams are out. Manchester City are obviously the strongest team left in there. This is what we wanted, teams to get a chance."
Full FA Cup quarter-finals draw
Fulham v Crystal Palace
Preston v Aston Villa
Bournemouth v Manchester City
Brighton v Nottingham Forest or Ipswich
The quarter-final ties will take place on the weekend of Saturday, 29th March.