German midfielder Mika Baur struck from close-range in the 52nd minute to settle a hard-fought clash with his first goal since arriving at Celtic from Paderborn in the summer.
Celtic boss Martin O'Neill was able to demonstrate the depth of the champions' squad ahead of Sunday's trip to Rangers in the Scottish League Cup quarter-finals.
Key players Camilo Duran, Benjamin Nygren and Kieran Tierney started on the bench and defender Cameron Carter-Vickers was given the evening off due to stiffness.
Although far from their best, Celtic did enough to close out a sixth consecutive league victory this term and their 13th in a row, stretching back to the closing weeks of last season.
O'Neill's men are five points clear of second-placed Rangers, who they also face in their next Scottish Premiership match at Celtic Park on September 20.
A dramatic last-gasp strike from substitute Bojan Miovski ensured Rangers kept within touching distance of their Old Firm rivals.
Back in the technical area after a two-game touchline suspension, Rangers boss Derek McInnes watched St Mirren goalkeeper Jacob Chapman keep his side at bay in the first half with a string of saves at Ibrox.
Rangers were dealt a massive blow in the build-up to the game with the confirmation that skipper Lawrence Shankland is out for three to four months with a hamstring tear, joining Portuguese striker Youssef Chermiti, out long term with a knee injury, on the sidelines.
But in the final seconds of normal time, Macedonian forward Miovski showed he might be able to fill the void, pouncing to grab the winner with a clinical finish as Rangers made it four successive victories.