Glasgow were only 6-3 adrift at half-time, but tries from Shane Horgan, Gordon D'Arcy, Dominic Ryan and Kevin McLaughlin gave Leinster a resounding bonus point win.
Man-of-the-match Fergus McFadden kicked 18 points, with Glasgow out-half Duncan Weir landing a seventh minute penalty for the visitors.
The Warriors enjoyed the best of the early territory, Chris Cusiter working his pack through the phases and they were rewarded with a long range penalty strike from Weir.
Sean Lineen's side came with a 'nothing to lose' attitude and 18-year-old debutant centre Mark Bennett was certainly not overawed, bursting through the Leinster defence in the 13th minute.
Tom Ryder, Richie Vernon and Johnnie Beattie led the charge up front, the Glasgow pack keeping their Leinster counterparts in check during the first quarter-hour.
A classy counter attack from Isa Nacewa, the Irish Players' Player of the Year, sparked Leinster into life and Ian Madigan probed with the boot, keeping the Scots pinned back in their half.
From a scrum in the 22, McLaughlin was held up close to the posts. But Ryder conceded a penalty for killing the ball and McFadden tapped over the simple penalty.
Weir was off target with a monster attempt from near the main stand, on the half-hour mark, and Glasgow had a narrow escape when Horgan looked to have scored in the right corner.
The big Leinster winger, having linked with Nacewa, avoided an initial challenge from DTH van der Merwe, but television match official Peter Ferguson ruled that he had a foot in touch when grounding the ball.
Leinster gained some consolation in the form of a 35-metre penalty from McFadden and Weir, with the last kick of the half, was narrowly wide from a difficult position to the right of the posts.
Beattie was pinged for holding on after trying to break from a scrum, allowing McFadden to kick the opening points of the second half.
Then came the game's turning point when Glasgow full-back Peter Murchie was sin-binned for coming in on the wrong side of a ruck. During his time off the pitch, Leinster scored 15 points.
McFadden kicked his third penalty and shortly afterwards, Madigan's high kick to the right was gobbled up by Horgan who managed to scramble over the line past van der Merwe.
McFadden added the extras to D'Arcy's 58th-minute touchdown, following a powerful burst from stand-in captain Jamie Heaslip. Glasgow stayed competitive, but Leinster had more in the tank.
Replacement David Kearney delighted the home crowd with two superb solo runs. His first attack almost led to a try for Heaslip. The second did, Ryan pouncing on a loose ball that Glasgow failed to deal with.
McFadden converted and did likewise after McLaughlin stormed through a couple of tackles and stretched over for Leinster's bonus point try.
Speaking afterwards, McFadden said: "We got a good going over at half-time, but we knew that it was going to be tough at time against Glasgow because it always is against them.
"Thankfully we got it right but there are definitely areas of improvement for us because things weren't clicking for us. We knew that if we kept our discipline that we could pull through and the lads showed great enthusiasm all week.
"We have a massive semi-final against Ulster and the talk in the dressing room in the aftermath was all about that game."
|Leinster Rugby Score Card|
|Glasgow Warriors Score Card|