Celtic beat 10-man Hearts 4-0 at Tynecastle on Sunday to book their place in Monday afternoon's William Hill Scottish Cup fifth-round draw.
The Championship leaders were up against it when midfielder Morgaro Gomis saw red following a rash challenge on Scott Brown after just eight minutes and Dutch defender Virgil van Dijk gave the visitors a half-time lead with a 29th-minute opener.
A flurry of goals early in the second period from John Guidetti (penalty), Anthony Stokes and van Dijk sealed the win for Ronny Deila's team.
In Sunday's earlier game, Rangers claimed a comfortable 3-0 victory over Kilmarnock at Ibrox.
Nicky Law opened the scoring with a deflected effort in 19 minutes and Kris Boyd added the second against his former before Law netted the third goal with a fine finish late on.
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