Kris Commons drove the champions into the lead in the third minute but Saints striker Gregory Tade levelled in the 18th minute before the visitors were denied what looked a clear penalty when Steven Anderson challenged Commons inside the box.
But Celtic were well off the pace all afternoon and in the 80th minute they paid dearly when former QPR striker Vine curled the ball in from the edge of the penalty area to hand the Perth club their first win of the league campaign.
Source: PA
Source: PA