Georgios Samaras put the visitors in front on 64 minutes and then Shunsuke Nakamura doubled their advantage, before substitute Cillian Sheridan added a third to put the game beyond St Mirren.
The visitors had the better of the opening play and should have taken the lead after only seven minutes when some neat play by Mark Wilson down the left set-up Scott McDonald, who forced Mark Howard in the St Mirren goal into an excellent save.
Then five minutes later, it was McDonald's turn to play in Andreas Hinkel, but once again Howard made a good stop to deny the full-back.
St Mirren had weathered the early Celtic storm and started to come back in to the game.
A Franco Miranda corner came back off the crossbar on 14 minutes and then a minute later came a pivotal point in the game when Artur Boruc was lucky not to receive his marching orders.
Craig Dargo latched on to a long ball out of defence and headed the ball past Boruc before the keeper brought him down on the edge of the box.
However, referee William Collum adjudged that it was not a goalscoring opportunity and only showed the keeper a yellow card, much to the frustration of the home support.
Celtic came back in to the game towards the end of the half and were unlucky not to find themselves in front at the break with both Glen Loovens and Scott Brown seeing chances from close range go just over the bar.
St Mirren piled on the pressure in the opening stages of the second half, but it was the visitors who took the lead with an excellent counter attack goal on 64 minutes.
A flowing move down the right saw McDonald play Hinkel in and the full-back played an excellent ball across the face of goal for Samaras to guide the ball home.
A minute later, Celtic doubled their advantage when Samaras fed the ball in to Nakamura, who side-stepped Miranda before firing a low shot past Howard from the edge of the box.
Celtic put the game beyond doubt on 80 minutes when substitute Sheridan tapped home for the third after a clever ball across goal by the unselfish McDonald.
The home side grabbed a late consolation through Jim Hamilton as Celtic looked to see the game out before their midweek trip to Denmark to face Aalborg in the Champions League.