Kris Commons had looked to have sent the Hoops on the way to victory with an early strike, but the Parkhead side's defensive problems were clear as they failed to record a victory for the third time in the opening five games of the season.
The Perth side came into the game after a virus had swept through Steve Lomas' side, but he was able to name an unchanged side, while his opposite number Neil Lennon gave a start to skipper Scott Brown before his side’s Champions League opener with Benfica, while he handed a debut to new boy Mixu.
The Hoops got off to the perfect start with three minutes on the clock as Gary Hooper found Commons on the edge of the area and the midfielder who was left out of the Scotland squad for last week’s double-header with Serbia and Macedonia, sent a message to Craig Levein by smashing the ball beyond Alan Mannus to put the Parkhead side into the lead.
St Johnstone could have been back level minutes later, but for the intervention of goalkeeper Fraser Forster, as the giant shot-stopper used his full frame in order to divert a free-kick from Dave Mackay away for a corner kick.
Lomas side did get level as Vine came in from the left wing and with no Celtic defender approaching him he was able to search out Tade on the edge of the area and with Charlie Mulgrew just behind him, the French striker managed to turn and knock the ball beyond Forster for the equaliser.
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The second half did not start in the same vain as the first, with most of the play in the midfield area, with the visitors having a couple of chances through both Commons and Hooper, but neither of them could find a way past Mannus.
Celtic continued to press forward, with Victor Wanyama miskicking the ball from 10 yards out after a cross from the left, then Brown having a shot easily saved by Mannus after he came in from the right-hand side.
With just over 10 minutes left in the game the Perth side took a shock lead as substitute Nigel Hasselbaink found Vine on the edge of the area and with Mikael Lustig offering the St Johnstone striker a huge gap, he used that and curled the ball beyond Forster in the Celtic goal.
The visitors continued in search of an equaliser and could have done so deep into injury time as substitue Tony Watt had a strike blocked by Mannus for a corner which was cleared as St Johnstone secured a famous victory.