Goals from Gary Hooper and Efe Ambrose, then Victor Wanyama's double, gave an under-strength Hoops side an unassailable interval lead against sorry-looking Saints.
Tony Watt scored with four minutes remaining to seal a commanding victory, which manager Neil Lennon would have wanted ahead of their Champions League Group G clash with Barcelona on Tuesday night.
Lennon will have some welcome selection headaches for Spain as his starting line-up had several key players missing. Skipper Scott Brown (hip), winger James Forrest (groin) and midfielder Kris Commons (hamstring) were out and striker Georgios Samaras was rested with full-backs Emilio Izaguirre and Mikael Lustig starting on the bench.
The SPL leaders might have started with a weakened side but they looked sharp and purposeful from the first minute when Buddies goalkeeper Craig Samson had to rush from his goal to foil Watt, who tried to latch on to a flick from Lassad.
Hooper was playing in an unfamiliar role behind Watt and Lassad but it made him no less of a goal threat and in the 15th minute he was perfectly placed to help the Tunisia international Lassad's cross into the net. Celtic's second came three minutes later when Charlie Mulgrew's whipped-in free-kick was spilled by Samson and Ambrose was on hand to scoop the ball high into the net.
Kenny McLean saw a tame drive saved by Forster before it was 3-0 in the 32nd minute when Matthews' deep corner from the right bounced off defender Paul Dummett straight into the path of Wanyama, who fired it low past Samson.
The rampant visitors should have made it 4-0 in four minutes later but Ledley headed another good Mulgrew free-kick over the bar from only six yards out. However, the next Celtic goal, and the best of the game, arrived in the 38th minute when Wanyama took a Mulgrew pass and from 30 yards curled the ball past the despairing Samson.
As the minutes ticked away the former Rangers striker headed a van Zanten free-kick wide of the target before flicking Jim Goodwin's cross over. But Celtic threatened continuously. In the 85th minute Hooper was too casual with his attempt at lobbing Samson when he clean through on goal, allowing the Saints keeper to save.
However, a minute later the tireless Watt got the goal he deserved when he bulleted a close-range header past Samson after being set up by Izaguirre.
Source: PA
Source: PA