Ballymena United's reward for beating Linfield on Saturday is a home Irish Cup quarter-final against Dungannon Swifts on Saturday, 1 March.
Holders Glentoran will host Ballinamallard or Glenavon but only if they defeat Armagh City in a replay.
Crusaders will be fancied to see off Ballyclare Comrades at Seaview.
Queen's University are through to the quarter-finals for the first time and the students are home to Warrenpoint Town or Bangor.
Irish Cup quarter-finals draw
Crusaders v Ballyclare Comrades
Ballymena Utd v Dungannon Swifts
Armagh City/Glentoran v Ballinamallard Utd/Glenavon
Queen's University v Warrenpoint Town/Bangor