Hefin O'Hare (left) scored the opening try for Glasgow
Glasgow: (13) 26
Tries: O'Hare, Lamont, Evans.
Pens: Parks 3
Leinster: (10) 20
Tries: D'Arcy 2
Cons: Contepomi 2
Pens: Contepomi 2
Glasgow sealed one of their best-ever victories to deliver a blow to Leinster's Magners League title hopes.
Hefin O'Hare's try put Warriors ahead before Felipe Contepomi replied with a penalty then matched by Dan Parks.
Rory Lamont touched down for Glasgow, but two soft tries by Gordon D'Arcy either side of the break appeared to put Leinster in the driving seat.
But two Parks penalties put Glasgow back in front before Thom Evans broke clear for a winning try.
The success at Hughenden was the Scottish side's first against the title-chasing Dubliners for five years.
Park missed with an early penalty attempt, but he then set up O'Hare with a perfectly-weighted long and looping pass following a quick Evans dash.
Argentine Contepomi eased the Leinster jitters as he slotted a penalty at the other end, but Parks replied in identical fashion.
And Glasgow increased their lead - albeit with a heap of help from the province.
Shane Horgan was the chief culprit when he sent a careless loose pass infield from the touchline.
Contepomi then failed to mop up a deft chip from Parks, allowing Lamont to pounce.
Glasgow's third try from Thom Evans proved crucial
Leinster began to apply some pressure and the Warriors lost Scotland back-row man Johnnie Beattie through injury.
They suffered an even bigger blow deep in stoppage time as Leinster were awarded a highly dubious touchdown.
Jamie Heaslip's floated pass to D'Arcy looked at least a metre forward, but Welsh referee Tim Hayes waved play on as the Irishman cruised under the crossbar, giving Contepomi a simple kick.
But the normally clinical kicker missed a simple kick after the break before D'Arcy completed his quickfire double by taking full advantage of some woeful tackling by the Glasgow back ranks.
Contepomi added the important goal, but Parks narrowed the gap to a single point with a well struck penalty and repeated the feat to snatch back the lead and set up a tense finale.
Hughenden erupted in the 62nd minute when Evans broke out of his own 22 before hoofing the ball ahead.
Horgan lost his footing in the race, leaving Evans to outpace Hickie for a great solo score.
Parks added the extras to give his side a nine-point cushion.
The drama intensified as Contepomi clawed back a penalty from point-blank range, but the Warriors staved off the late rally.
Glasgow: Lamont, O'Hare, Morrison, Barrow, Evans, Parks, Beveridge, Va'a, Thomson, Murray, Newman, Kellock, Swindall, Barclay, Beattie. Replacements: Tckachuk for Va'a (58), Lawson for Thomson (47), Wilson for Swindall (79), MacFadyen for Beattie (33).
Not Used: Turner, Gregor, Shaw.
Leinster: Dempsey, Horgan, D'Arcy, Warner, Hickie, Contepomi, Whitaker, Wright, Blaney, Green, Hogan, O'Kelly, Jowitt, Gleeson, Heaslip. Replacements: Kearney for Dempsey (77), Fitzgerald for Hickie (70), Corrigan for Green (55), Finegan for O'Kelly (50), McLaughlin for Jowitt (70).
Not Used: Vermaas, Easterby.
Ref: T Hayes (Wales).