Argentinian star Stortoni's injury-time try was enough to end the hopes of a Leinster side that relied largely on the kicking of their young fly-half Jonathan Sexton, who booted 12 points thanks to three successful penalties and a drop goal.
 
That haul was not enough, however, to get the Irish province back on track after their 52-23 hammering at the hands of the Scarlets last week. For Glasgow, their battling qualities most definitely shone through but the closeness of the result left their head coach Sean Lineen exclaiming: "I've got even more grey hair after that!"
 
It was an error-ridden start from both teams as they scrambled for the points that would see them hang onto the coattails of the Welsh leaders at the top of the league table. Leinster succeeded in getting off the mark first when a good spell of possession play led to Sexton firing them in front from 30 metres out.
 
On a night when Boyne clubman Shane Horgan, just back from the World Cup, became the first player from a junior club to captain Leinster at senior level, the visitors looked to dictate the pace but some stout defending from Glasgow meant try-scoring chances were limited and Sexton was called on again in the 25th-minute to crack his second penalty through the uprights.
 
Leinster's lead was reduced just after the half-hour mark when Glasgow fly-half Colin Gregor landed a neat drop goal, but the same player was off target with a penalty attempt on the stroke of half-time, as the Scots looked to make use of some decent territory late on.
 
Glasgow rallied at the break and came out looking their better side, with prop Moray Low managing to get over for the game's first try in the 46th-minute. It was the 22-year-old's first ever league try and came off a concerted drive from the home pack, which had been bolstered for the second half by the introduction of Scotland's World Cup hooker Fergus Thomson.
 
Gregor's conversion attempt was wayward and Leinster sought to muscle their way back into the lead with the introductions of Ireland's most-capped player Malcolm O'Kelly, promising prop Cian Healy and Ireland flanker Keith Gleeson for the closing 30 minutes. The trio did help Leinster get up a head of steam and the platform was laid for Sexton to land his third penalty of the night and send his side back in front.
 
Leinster moved 12-8 ahead when Sexton dropped a goal on the hour mark and although Gregor replied with a penalty effort from 25 metres out, replacement hooker Brian Blaney broke free into the hosts' 22 to lay off for the supporting Healy to charge over in the 69th-minute for his maiden league try.
 
Sexton missed the conversion though and Leinster had a final ten minutes to forget as O'Hare took a well-weighted pass from Stortoni to grab an unconverted try in the 73rd-minute and cut the visitors' lead to a single point.
 
A nail-biting finish ensued and it was Glasgow who had the final say as a cross-field kick from impressive replacement fly-half Scott Barrow exposed the Leinster defence and Stortoni, the man of the match, was on hand to claim the bouncing ball in the in-goal area and touch down for a hard-fought home win.