They broke Leinster's resistance only once in the first half with Argentinian full-back Bernardo Stortoni crossing for a 23rd minute try.
Dan Parks kicked two penalties and converted Stortoni's try for a 13-6 interval lead, with a spirited and youthful Leinster side staying in the hunt through the boot of Ian Madigan, who took over the place-kicking duties from late withdrawal Fergus McFadden.
Leinster's commitment to the cause could not be questioned and they kept plugging away right to the final whistle, but they got very few breaks on the night.
Madigan missed two kickable penalties in the early stages and flanker Paul Ryan had to be stretchered off after fracturing his fibula.
Worse followed as Ryan's replacement Dominic Ryan was rather harshly sin-binned before half-time, and Rhys Ruddock, Trevor Hogan and Mike Ross were all yellow carded in the second half as referee James Jones showed no mercy.
That left Leinster playing with 13 men for a time in the second half and Ross' late sin-binning saw the visitors end the game down to 14 and uncontested scrums were called for.
The sin-binnings did little for the game's flow. It was a scrappy encounter and Glasgow struggled to break Leinster down before pulling away through the boot of Parks and Rob Dewey's two-try salvo.
The result, which saw the Warriors complete a clean sweep of the Irish sides at Firhill Stadium this season, has moved Sean Lineen's men into second place and a step closer to a semi-final spot.
Leinster are already through to the play-offs and can nail down a home semi-final by beating Edinburgh at home in two weeks' time.
This contest did not look like a mismatch in the early stages, however, with Glasgow out of sorts and making some poor decisions, with experienced scrum half Chris Cusiter a notable sinner.
Leinster were unable to take advantage of their spritely start, however, missing two penalties inside 14 minutes through full-back Madigan.
Strong carries from Kelly Brown and Johnnie Beattie got the Warriors within scoring range, only for Leinster's defence to frustrate them. Indeed, Stortoni had a penalty reversed after clashing with tackler Eoin O'Malley.
But, as the rain began to fall steadily, Leinster's defence gave way on the 23-minute mark. Glasgow worked an opening on the right where Max Evans stepped inside, took contact and slipped a one-handed pass for Stortoni to touch down.
Parks, in probably his final match at Firhill before his summer move to Cardiff, landed an excellent conversion to take his career points' tally for the Warriors through the 1500-point mark.
Leinster enjoyed their best spell of continuity coming up to the half hour mark, helped by good work at close quarters from Trevor Hogan and O'Malley. With Fergus Thomson going off his feet at a ruck, Madigan opened his account with a close range penalty.
The former Ireland Under-20 international punished another ruck offence from the hosts, two minutes later. From just inside his own half, he launched a tremendous strike through the posts to make it 7-6.
Glasgow got the upper hand, though, as the first half came to a close. First, they threatened on the right once again, working some space for Max Evans to dart into, but he passed to his right when an inside ball to Colin Shaw might have led to a score.
Prop Ronan McCormack was penalised for taking out a lifter in the Glasgow lineout, allowing Parks to stretch Glasgow's lead back to four points.
In the 38th minute, the retreating Dominic Ryan produced an earth-shuddering tackle on Chris Cusiter as the Scotland captain burst into the Leinster 22.
Referee Jones ruled that Ryan had failed to roll away in a timely fashion. It was a harsh call as both players had taken punishment in the hit, but Glasgow undoubtedly deserved some reward for what was a well-executed attack which included two powerful runs from Beattie and Moray Low.
Parks kicked the resulting penalty to push his side into a 13-6 lead for half-time.
Scrum half Cusiter was in the wars, five minutes after the restart, as he was the victim of a high tackle from Hogan and the Leinster lock joined Ryan in the sin-bin.
Parks missed the place-kick and Graeme Morrison botched a certain try when he knocked on with only Madigan to beat, out wide on the left.
Glasgow were beginning to find their rhythm, nonetheless. They were territorially dominant now, despite some well-judged Leinster kicking, and hooker Thomson made good yardage before Leinster conceded another penalty and Parks' right boot made it 16-6.
Having been on the defensive for long stretches, Leinster's young guns were beginning to tire slightly and Glasgow used their physicality to good effect as the half wore on.
A sniping run by Cusiter led to Ruddock being sin-binned for failing to roll away after making the tackle, five metres from his line. It could be argued that the Leinster flanker had nowhere to go as the Glasgow forwards piled through. John Barclay was also fortunate not to be penalised for some reckless stamping.
With Hogan returning to the fray, Leinster's defending remained resolute. But it was only a matter of time before Glasgow created and finished a try-scoring chance.
Replacement Dewey, making his first league appearance since October, marked his return from injury with an almost immediate try.
The Scotland centre was on the pitch for just seven minutes when Glasgow secured lineout possession and he stepped his way past Dominic Ryan, powering his way to the line on a lovely diagonal run.
Parks kicked the conversion and also added the extras to Dewey's second score in injury-time, which came after Leinster prop Ross was sin-binned for pulling down a scrum.
Glasgow's patience was rewarded when Parks sent a cross-field kick over to the right corner. Michael Keating, who put in a workmanlike display, was unable to gather under pressure from two Glasgow players and the ball bounced up for Dewey to gleefully score.
Speaking after the game, Glasgow Warriors coach Sean Lineen said: "We'll take it. It's always hard to play against Leinster. They made it really difficult for us in the contact.
"The crowd were fantastic once again tonight. We needed more composure which we've struggled with over the past few weeks. But we'll take a win over Leinster any day."
Giving his post-match reaction, Leinster boss Michael Cheika admitted: "I never thought I'd be pleased with a 30-6 loss but I couldn't be prouder of the team. The Glasgow coach had said earlier in the week that nothing less than five points would be good enough, but the lads showed what playing for Leinster means to them.
"We were really disappointed with the referee and he didn't get much help from the other officials. I'm more disappointed for the young guys who put their hearts and souls into the game.
"We can be inspired by the effort and attitude tonight. We're still on top of the league and the Edinburgh game will be an important one for us.
"We're going to have to overcome a Toulouse squad next week who are probably going to be going into the game as favourites. We will take a lot of self belief from this game and that (performance) will charge us up for next week."
|Glasgow Warriors Score Card|
|Leinster Rugby Score Card|