Glasgow 21 Leinster 17: Leinster slumped to their second Celtic League defeat in succession as Argentinian Bernie Stortoni was the hero of Firhill as his last-gasp try stole the points.
With Leinster holding a narrow lead, the full-back barged over in the fifth minute of stoppage time to steal the glory.
The visitors were the first to establish any kind of rhythm and they edged in front with a penalty by Jonathon Sexton from 30 metres.
Leinster continued to hold the upper hand without looking like making a significant breakthrough. And they had to rely again on the boot of Sexton to increase their advantage in the 25th minute when Glasgow were guilty of handling in a ruck.
The bulk of the action was being fought out in midfield but the Warriors got up and running on the half-hour mark when stand-off Colin Gregor clipped over a smart drop-goal.
Gregor was back in the spotlight on the brink of the break but this time it was for negative reasons as he sent a penalty attempt wide of the target after Andy Newman had been illegally challenged at a line-out.
Glasgow forwards coach Shade Munro sent World Cup hooker Fergus Thomson into the fray immediately after the restart in place of Eric Milligan.
The switch seemed to inspire the Warriors and within four minutes they surged ahead thanks to a try by prop Moray Low following a pack drive.
It was a moment of joy for the front-row youngster, who had seen a score chalked off earlier.
Leinster shrugged off the setback to snatch back the initiative as Sexton completed his penalty treble. And he delivered another dent to the Glasgow morale by adding a drop-goal to his tally.
Gregor set up a tense finale by thumping over a 25-metre penalty.
Cian Healy put Leinster back in control when he pounced for a try against the run of play.
But substitute Hefin O'Hare went over at the other end to give the Warriors a fresh dose of hope.
And then Stortoni was in the right place at the right time to settle the issue.