St Mirren gave Celtic an early Scottish Cup scare before the Hoops sealed their place in the semi-final with a 4-1 win.
Harry Davis stunned Celtic Park by giving the Championship's bottom side the lead against the runaway Premiership leaders in the 13th minute.
The Buddies held firm and were the first side since Barcelona in November to hold a half-time lead at Celtic Park.
The Saints might have been 2-0 up in the second half when Stevie Mallan's free kick deflected off the crossbar, but after the hour the Hoops turned on the style.
Substitute Patrick Roberts' free kick was headed in by Mikael Lustig in the 58th minute, the Paisley side barely had chance to draw breath before Scott Sinclair curled a shot into the far corner from the left side of the box to give Celtic the lead.
A Moussa Dembele tap in and a 25-yard strike from Leigh Griffiths put some shine on the result for Brendan Rodgers' treble chasers.