Peter Horne snatched a draw with a touchline conversion in the closing stages of one of the most dramatic Pro12 games in years.
The Warriors seemed poised for a superb victory when they carved open the home defence to race into a 27-7 interval lead on a perfect night for rugby at the RDS.
But it was Glasgow who were left trying to salvage something from the game after champion Leinster blitzed them in the second-half, with replacement scrum-half Isaac Boss leading the way with two tries.
In the end both sides secured try bonus points and netted three points each as the battle for semi-final spots in the Pro12 looks set to go down to the wire.
Glasgow looked set for a facile win when they led 27-7 at the interval but Leinster came storming back in the second-half and hit the front in the closing stages.
Gregor Townsend's men were well worth their 27-7 interval lead after running in three converted tries in a superb display of attacking rugby.
Leinster coach Matt O'Connor bemoaned the fact that his frontline Irish internationals were not released to play and they could have done with leadership on the field.
Glasgow dictated matters from the outset with scrum-half Niko Matawalu once again controlling the game.
It was no surprise when they hit the front after eight minutes when strong running from Richie Vernon created the opening which was finished by Hogg.
Peter Horne added the extras and made it 10-0 after 12 minutes when he landed a penalty from the left after his captain Ally Kellock was taken out in a lineout.
Leinster finally got moving and pressed forward and while forays by Dave Kearney, Tom Denton and Mike McCarthy were well defended, the champions kept the pressure on.
Good work by scrum-half Eoin Reddan, Shane Jennings and Jimmy Gopperth sent Fergus McFadden over for a fine try in the right corner, which Ian Madigan converted to make it 10-7 after 25 minutes,
But it was all Glasgow from there to the break and Leinster struggled to cope with their strong midfield running.
Vernon got their second try nine minutes from the break after a good break down the right by Tommy Seymour.
Horne kept the scoreboard ticking over with the conversion and it got better for them five minutes from the interval when Mark Bennett ran through a sleepy defence for their third try.
Horne again converted and Glasgow continued to make the most of every opportunity with Bennett landing a penalty from 40 metres on the stroke of half-time to lead by 27-7 at the break.
It didn't take Leinster long to hit back after the restart with replacement scrum -half Isaac Boss charging down a clearance from Glenn Bryce to score in the left corner less than a minute into the second-half.
Madigan converted from the left and then added a penalty as they piled on the pressure to reduce the margin to 27-17 after 47 minutes.
Glasgow tried to regroup but indiscipline cost them dearly when Matawalu was binned for lashing out after he was held by Cian Healy, with the Irish international having come on at the break along with Sean Cronin, while another of their Six Nations heroes Luke Fitzgerald was also drafted in.
Leinster scored from the attack following Matawalu's card in the middle of the field with Jordi Murphy slicing open the visitors' defence and Madigan adding the conversion to cut the lead to 27-24 aftr 52 minutes.
Leinster used their extra man to devastating effect with Boss showing all his experience to dummy and race through for his second try just when they were lined up to go wide.
That netted the bonus point for the champions as Madigan opened up a 31-27 lead with 25 minutes remaining.
Glasgow did not give up and were rewarded six minutes from time when they got their fourth try after going wide following a sustained bout of pressure for Bryce to score.
Horne kept his nerve to land the touchline conversion from the left and secure a dramatic share of the spoils.
Leinster: Z Kirchner; F McFadden (L Fitzgerald 53), B Te'o (G D'Arcy 72), I Madigan, D Kearney; J Gopperth, E Reddan (I Boss 33); M Bent (C Healy 40), R Strauss (S Cronin 40), M Moore (T Furlong 53); T Denton, M McCarthy; J Murphy, S Jennings, J Conan (D Ryan 66).
Scorers: Tries: I Boss (2), F McFadden, J Murphy. Cons: I Madigan (4). Pens: Madigan (2).
Glasgow Warriors: S Hogg (G Bryce 39); T Seymour, M Bennett, R Vernon (C Braid 43), DTH van der Merwe; P Horne, N Matawalu (H Pyrgos 62); A Allan (J Yanuyanutawa 62), F Brown (Strauss 67), Z Fagerson (M Cusack 10); T Swinson, A Kellock (J Gray 53); R Hartley, C Fusaro (P MacArthur 47), J Strauss (A Ashe 59).
Scorers: Tries: S Hogg, R Vernon, M Bennett, G Bryce. Cons: P Horne (3). Pens: Horne, M Bennett.
Referee: N Owens (WRU).
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