Leinster made sure of a place in the last eight of the Heineken Cup with a bruising win away to Glasgow.
The home side made most of the running in the first half but only had two Duncan Weir penalties to show for their efforts, with the game tied at 6-6.
After the interval, Rob Kearney grabbed a try for the defending champions, with Colin Gregor replying for the hosts.
Issac Boss powered over for the decisive score late in the game to end Glasgow's hopes of qualification.
Leinster were far from their best and, having lost Sean O'Brien to a yellow card for the final five minutes, had to defend like lions to close out their victory.
Glasgow will be frustrated after squandering a number of good opportunities but lacked composure and an inventive spark in the opposition 22.
Sean Lineen's side were spirited throughout and Leinster were rattled in the opening exchanges, failing to find their range on the tight Firhill pitch.
With Scotland locks Al Kellock and Richie Gray bulldozing forward at every opportunity, Glasgow were on the front foot.
But handling errors and some poor distribution from fly-half Duncan Weir meant they could not build constructively on their menace.
Weir slotted over a penalty before he failed with a drop-goal attempt on 16 minutes, having had to readjust from a poor set-up throw from Chris Cusiter.
Jonny Sexton levelled with a long-range effort a few minutes after slicing wide from much nearer the posts.
Weir knocked over a straightforward penalty to restore Glasgow's lead, with Leinster still struggling to find any fluency.
It took 35 minutes for the European champions to get within range of the try line and 26 phases of possession had passed before Sean Cronin was stopped inches from the base of the post by Gray.
And to a huge cheer from the home crowd, Glasgow stole the ball against the head at the resulting five metre scrum.
But the Dubliners were level again with the last kick of the half, Fergus McFadden knocking over the penalty.
The second half was just a few minutes old when a chip from Sexton bounced favourably for the onrushing Kearney, who brushed past the less than convincing Stuart Hogg to run in a simple try. McFadden added the extras.
Weir reduced the deficit with a simple penalty but the visitors were looking more dangerous in attack and McFadden was brought to halt just short of the line following an electrifying break.
The centre then kicked Leinster further ahead after Glasgow tighthead Ed Kalman was penalised for not binding at a scrum.
Glasgow were given fresh impetus by a slew of substitutions and Gregor, on for Cusiter, took a neat offload from Colin Shaw to wriggle over in the corner.
And Weir converted from the touchline to level with 16 minutes remaining.
Leinster responded by turning over possession from Johnnie Beattie and Heinke van der Merwe charged on to set up a move from which Boss squeezed in the winning try. McFadden was again accurate with the conversion.
Glasgow rallied again but a fumble from Graeme Morrison and Hogg choosing to go it alone when he had team-mates in support were to prove costly.
O'Brien was shown a yellow card for infringing on the floor 10 metres out from his own line, reducing Leinster to 14 men for the final five minutes but Glasgow could not breach a well-organised defence.
Glasgow head coach Sean Lineen: "Leinster are not the Heineken Cup champions for nothing.
"I thought we stood toe-to-toe with them for long periods of the game.
"One bit of class from Kearney, try. We had two guys there, but he got the ball. That's just class.
"It's out of our control now. There are a couple of things that have to happen in a couple of the other groups for us to be involved in the Amlin."
Leinster head coach Joe Schmidt: "I'm delighted to get the result. I know there were imperfections in the performance and I know my players have gone on record saying I'm always fussy.
"I don't really care about the imperfections today. I just think you deserve to be proud of what you did.
"You deserved to get the four points and we'll come away from this, glue ourselves back together in six days' time and front up at the RDS in front of a full stadium and try to chase that home quarter-final that we really, really want."
Glasgow Warriors: Lamont, Seymour, Hogg, Morrison, Shaw, Weir, Cusiter, Welsh, MacArthur, Kalman, Gray, Kellock, Harley, Fusaro, Barclay. Replacements: Nathan for Shaw (62), Wight for Weir (74), Gregor for Cusiter (59), Hall for MacArthur (56), Ryder for Gray (61), Beattie for Barclay (61). Not Used: Reid, R. Grant.
Leinster: R. Kearney, D. Kearney, McFadden, D'Arcy, Nacewa, J. Sexton, Reddan, Healy, Cronin, Ross, Cullen, Toner, O'Brien, Jennings, Heaslip. Replacements: O'Malley for D. Kearney (64), Boss for Reddan (59), van der Merwe for Healy (64), White for Ross (66), Browne for Cullen (74), R. Ruddock for Jennings (59). Not Used: Dundon, Madigan.
Ref: Nigel Owens (Wales).