It took a penalty by Barry Robson just after the hour mark to separate the teams.
Indeed if Billy Mehmet's shot for the visitors just after half-time had gone in rather than come back off the post there may have been a shock victory for St Mirren.
It was the visitors that threatened first when Garry Brady wrong-footed Paul Hartley before firing in a shot which Artur Boruc gathered comfortably.
Jan Vennegoor of Hesselink was crowded out as he threatened to force his way through before Stephen McManus's header from Hartley's free-kick was held by Mark Howard.
The Buddies were passing the ball well and Celtic were finding it hard to gain possession. Their frustration was obvious when Scott McDonald elected for a long-range shot which drifted wide when there was better-placed team-mates.
Franco Miranda curled in a dangerous cross which caught Tom Brighton and Mehmet flat-footed as St Mirren continued to play well.
Just before half-time Aiden McGeady burst into the match but his two efforts were deflected for corners.
Saints went so close to taking the lead just after the interval. A flowing move ended with Brighton's pass finding Mehmet whose strike on the turn hit the post before Stephen O'Donnell's effort from the rebound was diverted for a corner.
Celtic increased the tempo after the scare and Gary Caldwell's header from Lee Naylor's free-kick was well-saved by Howard.
Central defenders Will Haining and John Potter, who had played so well up to that stage, then got themselves in a tangle which allowed Vennegoor of Hesselink to advance on goal. As the Celtic striker shot he was pulled back by Haining who was sent off.
Robson's well-struck penalty was bravely blocked by Howard but had just crossed the line before being hooked clear.
Saints never gave up trying for an equaliser and O'Donnell flashed his shot just wide and substitute Marc McAusland headed over Antonio Tonet's corner.
Celtic also had chances to increase their lead but in the end Robson's penalty was enough to give Gordon Strachan's side a winning start to their campaign.