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.
Saints boss Danny Lennon made one change and reshuffled his team, with defender David Barron coming in for striker Sam Parkin - who started on the bench. However, his men were crushed in a one-sided first half.
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.
In the 13th minute Hoops keeper Fraser Forster was forced into a decent save at his near post from Lewis Guy's volley after a great curling cross from Buddies' midfielder David van Zanten had picked out the unmarked Paisley striker.
Moments later, at the other end, Celtic's stand-in captain Joe Ledley's drive was more easily saved by Samson but the Saints number one was soon to be beaten twice in three minutes.
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 before entertaining the Hoops fans with a quadruple somersault celebration of his first goal for the Parkhead club.
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.
Celtic looked in the mood to pile on the misery for Saints but Ambrose missed a great chance to grab his second when he headed over.
Unsurprisingly, St Mirren manager Danny Lennon made a change at the break with Dougie Imrie replacing Barron while Izaguirre came on for Kelvin Wilson, with Mulgrew moving into the centre of defence. Celtic then replaced Lassad with Miku.
The Parkhead men continued to pepper the Saints goal with efforts and in the 63rd minute van Zanten prevented Wanyama taking home the match ball when he headed clear the midfielder's goalbound header from Matthews' corner.
In the 67th minute Steven Thompson had a point-blank shot saved by Forster before Carey blasted the rebound wide.
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.
Wanyama came close and Samson saved Hooper's close-range header as Celtic finished with a flourish to reinforce their place as the top team in Scotland, although they will undoubtedly find it more difficult against Barca.