The Leinster fans roared their side into the RaboDirect PRO12 final for a fourth consecutive year, but there were notes of relief in their chants at the finish after Glasgow narrowed the gap dramatically with a 75th-minute try by Mark Bennett and were only denied the period of extra time their efforts deserved when Stuart Hogg's conversion attempt drifted just wide.

It was a stirring finish to a startling season by Glasgow, for they played with the bold spirit that has characterised their approach since last September. They threw themselves heart and soul into this game and left nothing on the pitch at the end. Coach Gregor Townsend and captain Al Kellock may have been distraught at the final whistle, but they will find many reasons for pride and optimism as they reflect on the PRO12 campaign as a whole.

Kellock had warned of the dangers of sitting back and admiring opponents and his players had clearly taken his message to heart as they tore into Leinster in the opening quarter. The Warriors were quicker in thought and deed than their Irish opponents and were not flattered one bit by the 7-3 lead they held at the end of that period.

Nor was it any great surprise that their advantage rested on a moment of quick-wittedness by Niko Matawalu, the Fijian scrum-half who was named Glasgow's Player of the Season last week. With 15 minutes on the clock, and with Leinster leading 3-0 from a Jonny Sexton penalty three minutes earlier, Matawalu feigned a pass to the right near the Leinster posts and simply dotted the ball down for a try.

Hogg's conversion, and a penalty soon afterwards, gave Glasgow a seven-point lead, but it was narrowed a little later when Leinster put in a typical forward surge from a line-out on the left side, made a 10-yard gain, then unleashed Jamie Heaslip from the maul to power over for a try.

Sexton missed the conversion, but the Lions fly-half clipped over a penalty a few minutes later to put Leinster back in front. More ominously, Glasgow had just lost Matawalu to the sin-bin for a silly offside offence, and they would lose Josh Strauss with an unspecified injury soon afterwards. Suddenly, the visitors found themselves up against the European champions without their two most influential players.

In which circumstances, they did well to hold on until half-time without taking more damage on the scoreboard. Indeed, with 14 men on the pitch – Rob Harley had come on to replace Strauss – Glasgow were still setting the pace at the end of the half, mounting a stirring attack deep into Leinster territory in the final moments before French referee Pascal Gauzere blew for the interval. Leinster showed their expected ferocity in contact and caused panic in the Glasgow ranks at times with sudden injections of pace, but much of what they did lacked the precision and accuracy that might be expected of reigning European champions.

Glasgow also made sure that Sexton did not have the armchair ride he so often enjoys at the RDS, a strategy that meant that Leinster's outside backs also had to work harder than usual to get on the ball.

Hogg and Sean Maitland made a couple of decent runs in the third quarter, but the scoreline stuck at 11-10 in Leinster's favour. Yet still Glasgow played with more adventure and more wit, Matawalu clearly unaffected by his time on the naughty step as he tried to spark his side into life with sniping runs. Ryan Wilson, at No 8, also made some conspicuously effective contributions, although too much of Glasgow's most creative play took place in the middle third of the pitch and did not threaten the Leinster line.

That pattern appeared to gird Leinster's resolve and the Dubliners took advantage in the 63rd minute when Sexton hammered over a penalty from near the 10m line. Another effort, two minutes later, might have killed Glasgow stone dead, but it rattled off the left upright and the Scots breathed again.

Not for long, though, as Sexton drove his next effort, from near half-way, straight between the posts. That put Leinster ahead by the distance of a converted try, but Glasgow closed the gap dramatically when a Matawalu tap-penalty move was carried on by Ruaridh Jackson and Ryan Wilson, for Bennett to surge over for his score.

Hogg had kicked brilliantly earlier in the game, but his mental tape measure failed him at the critical moment and Glasgow's dreams of glory were over for another year.

Leinster: R Kearney; F McFadden, B O'Driscoll (A Conway 12), G D'Arcy (I Madigan 68), I Nacewa; J Sexton, I Boss; C Healy (J McGrath 72), R Strauss (S Cronin 40), M Ross (J Hagan 61), L Cullen (capt), D Toner, K McLaughlin, S Jennings (R Ruddock 72), J Heaslip.

Glasgow: S Hogg; S Maitland (R Jackson 60), S Lamont, A Dunbar, DTH Van der Merwe (H Pyrgos 70); P Horne (M Bennett 67), N Matawalu; R Grant (M Low 25 - 32; E Kalman 62), P MacArthur, J Welsh (M Low 40), T Swinson (T Ryder 12 - 23; 67), A Kellock (capt; T Ryder 60 - 67), J Strauss (R Harley 35), J Barclay, R Wilson.

Referee: P Gauzere (France)