Ireland duo Brian O'Driscoll and Gordon D'Arcy bagged closing quarter tries to earn Leinster a place in the last four of the Celtic Cup on Friday night.
Glasgow almost caused an upset at Lansdowne Road as Leinsters credentials came under severe second-half pressure from the Scots.
It took the elusive running of British & Irish Lions pair ODriscoll and DArcy to send the province to a 33-24 win - and into a probable semi-final clash with Munster.
DArcy was also on target in the first half as Leinster ran up a 21-3 lead by the 35th minute.
Glasgows reply was measured to say the least as Dan Parks chopped over his second and third penalties in injury time.
But Hugh Campbells side rampaged right back into it on the restart as Paul Dearlove and Sean Lamont charging through on an 80-metre run helped Glasgow level things up.
The visitors even went 24-21 ahead as Scotland international Parks kicked his fourth penalty, yet ODriscoll and DArcy were on hand to wrestle back the initiative.
After Parks had sent a sixth-minute penalty to the right, Leinster burst through for the opening try as an ODriscoll and DArcy set-up saw Girvan Dempsey cross in the left corner.
David Holwell converted and sandwiched a Parks penalty with the convert of retiring number eight Victor Costellos 17th-minute lunge over.
A long Holwell skip pass sent DArcy jinking through the Glasgow cover for his first score five minutes before the break.
However, poor discipline from the home side saw Parks give Glasgow a window back into it as he chipped over two late penalties for a 21-9 deficit at the break.
With three more Lions namely Malcolm OKelly, Shane Horgan and Denis Hickie thundering out for the second half, Leinster seemed certain to wrap things up.
Two minutes in, though, number eight Dearlove ended a neat Glasgow move with a try in the left corner.
As the pace quickened, Leinster set up field position and a galloping surge from OKelly almost saw him stretch over.
From the next phase, Glasgow scrum-half Sam Pinder caught the home side napping as he sent 51-cap wing Lamont scurrying over with Horgan in hot pursuit and in under the Leinster posts.
ODriscolls first cup try set up by Des Dillon after 64 minutes and DArcys muscular shunt under the posts six minutes later ended the Glasgow fight.