They made history with the nine consecutive wins that brought them here, but they were running on empty long before the end. Leinster might have been a little flattered by the margin, helped as they were by two tries in the last six minutes, but they were comfortably the better side and fully deserving winners.
Brian O'Driscoll, playing his last-ever game of rugby, was given thunderous ovations by the adoring Leinster crowd at the beginning and the end, but it was a hugely disappointing swansong for the legendary centre as he was crocked by an early calf injury and hobbled off after just eight minutes.
O'Driscoll will take many better memories into retirement, and leave many behind as well. We witnessed the passing of a great last night, and if his parting shot was more of a whimper than a bang it will do nothing to erase his status in the game. Rugby has one less genius this morning.
Glasgow were gutsy and courageous, but they were also a critical notch below Leinster in too many areas. They were also dishevelled by a spate of early injuries, and their bench was bare long before coach Gregor Townsend would have liked. They strung together a few decent passages of play, but they foundered all too often and all too easily on the rocks of Leinster's stonewall defence.
The message from the Glasgow camp had been that they still had something in the tank after their epic semi-final victory over Munster a fortnight ago, but they looked drained at times in this game. Energy levels have rarely been an issue for Glasgow over the past couple of seasons, but they were never the equals of Leinster here. Leinster were carried along on a wave of emotion and the rapturous support of their crowd. Glasgow's followers pumped up the volume as well, but, like their side on the pitch, they were always going to lose the battle of the tonsils in the stands.
Leinster were also sharper in everything they did. They made a few uncharacteristic errors early in the game, and they were clearly disrupted by O'Driscoll's departure, but they settled into a compelling rhythm that recalled their Heineken Cup-winning side of a couple of seasons ago and they muscled Glasgow out of the game.
You expect Leinster to be fierce in contact, but the body count was mounting long before half-time. By then, Leone Nakarawa had taken over from Chris Fusaro, Dougie Hall had made way for Pat MacArthur and Ruaridh Jackson was on as a blood replacement for Peter Horne. But there was more than that to Glasgow's defeat, because they made far too many errors to put themselves in with a shout of winning. There were four or five moments when Glasgow had Leinster on the rack, but knock-ons and poor decision-making cost them each time.
Yet credit to Leinster, for they took advantage superbly. In the first half, when the game was still a close-fought contest, they put themselves in a position of strength with two well-taken tries. For the first, after 16 minutes, they absorbed a period of Glasgow pressure before unleashing themselves upfield and sending Zane Kirchner over in the left corner, while the second came two minutes before half-time when Kirchner turned provider, sending Shane Jennings through the middle on an unstoppable blast to the line.
The scores were crisp and well-taken, but they still reflected badly on the Glasgow defence. The Warriors have mostly been outstanding in that area this season, so they picked a bad moment to suffer a lapse. The second try was the real killer, however, as they had actually dominated the second quarter and had pulled Leinster all over the park. From that point on, it was an uphill battle.
Finn Russell did cut into the deficit when he struck his fourth penalty just before the break to take the interval scoreline to 14-12 in Leinster's favour.
But it was almost a last note of defiance, for Leinster turned the screws early in the second half and never really let up from that point on. Glasgow's effort level probably deserved some points in that period, but it was clear to see that the energy was draining out of them the longer it went on.
The errors continued to mount, and so, too, did the desperation in Glasgow's ranks. Penalties were bound to follow, and Jimmy Gopperth, Leinster's admirable fly-half, nailed two of the three chances he was given. That took Leinster to 20-12, meaning Glasgow needed more than a converted try to get back in front. In the circumstances, it was inevitable that caution would desert their game.
As it went, Leinster punished them again. Kirchner collected his second try with six minutes left on the clock and Gordon D'Arcy twisted the knife with Leinster's fourth a couple of minutes later. A cruel end for Glasgow, but given the strength of their squad, it is an experience that is more likely to make them than break them.