Norwegian midfielder Stefan Johansen opened his Hoops account with a close-range header a minute before the interval.
Striker Leigh Griffiths grabbed the second goal in the 61st minute before strike partner Anthony Stokes grabbed the third in the final seconds to put a true reflection of the Hoops' superiority on the scoreline.
Celtic will wrap up their third successive championship with a win against Partick Thistle at Firhill on Wednesday night, if second-placed Aberdeen - who beat Kilmarnock 2-1 at Pittodrie on Saturday - drop points at Ross County the previous night.
Danny Lennon's St Mirren side, meanwhile, remain mired in trouble at the wrong end of the table although they can probably take some confidence from their first-half performance.
On the face of all available evidence, though, there was never any real chance of a St Mirren upset.
The Buddies went into the game in the relegation pay-off spot and had not won at Celtic Park since 1990.
However, it was Celtic goalkeeper Fraser Forster who had to make the first real save of the game in the sixth minute when he had to dive to his right-hand post to stop a low drive by Paul McGowan, after the former Celt had been set up by Conor Newton.
That close call boosted the visitors who began to move forward with some belief and purpose, but there were Celtic chances before the first goal arrived.
Griffiths, the game's most influential player, had a drive saved by Buddies goalkeeper Marian Kello and then had the ball in the St Mirren net just after the half-hour mark, only to see the flag up for offside.
St Mirren had chances and half-chances of their own, one of which came when a mistake by Charlie Mulgrew saw the Celtic defender's clearance land at the feet of right-back Jason Naismith but his angled drive sped straight to Forster.
But St Mirren's valiant first-half effort was undone in the 44th minute when Griffiths went racing down the right before sending in a cross which Johansen only had to guide past Kello from 10 yards for his first goal since signing from Stromsgodset in January.
There was no real evidence, either on the day or historically, that the Paisley side would turn it around after the break.
Kello had to make a save from Liam Henderson seven minutes into the second half, by which time Celtic were turning the screw. They made sure of the points when Stokes' pass to Griffiths was confidently slipped past Kello by the Scotland striker.
The Buddies were deflated as the home side sniffed more goals in the air.
Kris Commons had a shot saved by Kello before an angled drive by the Hoops attacking midfielder crashed back off the post.
In the 71st minute Stokes headed into the net from an Adam Matthews cross but Commons was penalised for his challenge on Kello.
Griffiths missed a great chance in the 81st minute when he was set up inside the box by skipper Scott Brown, all too casually chipping the ball over Kello but also wide of the far post, yet it mattered little.
Celtic defender Virgil van Dijk had the ball in the net from a Stokes cross only to be ruled offside before substitute Teemu Pukki, on for Commons, drove wide of the target when he ought to have made Kello at least make a save.
There was still time for Stokes to drill the ball low past Kello from the edge of the box for a well-deserved third.