
In a game filled with late drama, Giorgos Giakoumakis' dramatic goal with virtually the last kick of the game was the difference in Celtic's win.
Alex Mitchell had scored for the Perth side in the 92nd minute after Andrew Considine's own goal, but the champion went up the other end and scored again.
Alex Bernabei's cross was pounced on by Giakoumakis to extend Celtic's lead.
The gap can be narrowed by Rangers if they win at home against St Mirren.
Celtic showed great character after Mitchell's sucker punch, but once again they were wasteful when on top. They were frantic and nervy when the cavalry was thrown on them.
They had 80% of possession for the first 70 minutes, but in the first half they struggled to penetrate a stout Saints defence, until a clever inside run and low cross from Sead Haksanabovic forced Considine to turn past his own goalkeeper just before the break.
The Celts created more chances after the break, with Giakoumakis and Daizen Maeda both having goals ruled out for being in an area where they shouldn't have been.
Stevie May forced Joe Hart to tip his shot onto a post, and then the strikers crossed forConnor McLennan, who should have done better from eight yards.
The reward was fleeting. Ali Crawford's free-kick caused havoc, and Mitchell was there to side-foot home.
They will kick themselves at the end.
With three minutes to go, Celtic worked the ball down the side to Bernabei, whose cross was headed home by Giakoumakis to give them the victory.

In the first six games of the season, Celtic fired up. They are not finishing the chances they are creating and there seems to be a slight drop in intensity.
Postecoglou made six changes, with the captain missing the first game due to an injured ankle.
fringe players must step up in order to keep winning There were some positive signs.
Haksabanovic and Bernabei started at left-back in the absence of Greg Taylor. It could be a tough spell because of the commitments and the absence of their skipper. Celtic showed that at the death.
They can be counted on to be unfortunate. They were unlucky to lose the game to an own goal. The kitchen sink was thrown at Celtic in the last quarter as they failed to convert chances.
The Saints look a lot better than they did a year ago, and could potentially threaten the top six.
Celtic and St. John's are both away to Livingston next Saturday, while the other is at home to Hibs on Saturday.