John Guidetti scored a hat-trick, Leigh Griffith grabbed a double, while Emilio Izaguirre netted his first goal for four years in a match which Thistle played the second-half with 10 men after the dismissal of Stuart Bannigan.
Guidetti struck his first with a superb free-kick from just outside the box which left Scott Fox with no chance as the ball hit the top corner of the net moments after the striker had been impeded on 31 minutes.
Thistle were reduced to 10 men a minute before the break when Bannigan crashed straight through Guidetti from behind, leaving referee Kevin Clancy with little option but to dismiss the midfielder.
Izaguirre scored a rare goal three minutes after the break when Tony Stokes flicked a backward header into his path for the full-back to volley the ball past Fox.
Four minutes later Guidetti scored a more spectacular free-kick when he smashed the ball into the roof of the net past the static Fox from 25 yards
And Guidetti (56) was involved again when he was brought down in the box by Abdul Osman, ad he brushed himself down to send the keeper the wrong way from the resulting penalty.
Griffiths (52) got on the scoresheet shortly after coming off the bench when he met an Izaguirre delivery at the back post to nod home.
And the substitute was on target again six minutes later when he closed down Fox, whose attempted clearance struck the Celtic forward’s leg and spun over the line.
Stokes should have given Celtic the lead on 13 minutes after Mikael Lustig crossed to the back post but the unmarked striker sent his header back across the face of goal and wide of the target.
Eight minutes later Lustig got on the end of a delightful delivery from Stefan Johansen but Fox did well to get down to his near post to save.
In between those chances Thistle came close on the counter-attack which ended with James Craigen flashing a drive narrowly wide of the far post.