With the Scottish side scoring just one win in their previous five encounters with Munster, this was a very encouraging result for Sean Lineen and his players.
Speaking afterwards, a delighted Lineen said: "That was a really hard game of rugby. I can't speak highly enough of the front five.
"I've never seen a Glasgow side scrummage like that during my time in charge.
"We refused to get soaked into the arm wrestle that Munster wanted. They tried to force a few of our guys into being sin-binned, but they ended up losing a few of their own instead.
"It was a real battle and we came out on top."
The only blip on the night for Glasgow was that replacement fly-half Ruaridh Jackson dislocated his shoulder in the act of scoring the game's only try, 12 minutes from the end.
The positives were few and far between for Munster, but debutant full-back Felix Jones grew into the game and Lifeimi Mafi, Denis Fogarty and Donnacha Ryan carried well throughout.
Things might have turned out differently had the champions built on some early pressure near the home line and scored a try.
Dan Parks sliced an up-and-under and Munster piled forward with Mafi, Doug Howlett and Tony Buckley all making darts for the whitewash.
But Glasgow's defence was resolute and summed up by tough-tackling prop Jon Welsh, who was making his first Magners League start.
The confidence carved out by last weekend's friendly win over London Wasps took its time to show, and the Warriors fell 3-0 behind courtesy of a Jeremy Manning penalty.
New Zealander Manning got a chance to impress in the Munster number 10 jersey, with Ronan O'Gara still in pre-season training and Paul Warwick out injured.
With the Munster scrum struggling and Glasgow's pace causing problems out wide, Manning was not allowed to influence the game as he wanted.
Sparky runs from Tom Evans and Bernardo Stortoni got the home crowd going and Parks levelled matter with a 13th minute penalty.
Munster, despite some expansive play out wide, were out of sorts and Glasgow continued to impress with ball in hand - experienced internationals Chris Cusiter and Graeme Morrison relishing the chance to test the champions' midfield defence.
There was a flare-up between the forwards after Cusiter looked to have been taken out in the air as the sides maintained the high pace of the opening quarter.
Glasgow were transferring their dominance onto the scoreboard via the right boot of Parks, who fired over three more penalty goals in the first half.
His last one, on the cusp of half-time, came after referee James Jones lost his patience with Munster and sin-binned scrum half Peter Stringer for killing the ball at a ruck.
12-3 down at the break, Munster need to fire back on the restart but it was Glasgow who charged back on the attack.
Welsh raised the ante with a great run down the left wing which led to an unsuccessful penalty from Parks, after a deliberate offside from Munster's stand-in captain Mick O'Driscoll.
Tony McGahan's side clawed their way back into contention with two penalties from Manning to cut the gap to just 12-9.
Reinforcements arrived for the visitors in the form of recent signings Julien Brugnaut and Toby Morland, yet Glasgow were quick to dash the Irish side's hopes of a comeback.
Manning added to Munster's woes by getting sin-binned for playing the ball on the ground and Parks mopped up by striking his fifth and final penalty.
Youngster Ruaridh Jackson came on in a half-back switch and was immediately involved in the match-deciding try.
Argentinian Stortoni launched a counter attack, on 68 minutes, running back a loose kick. He combined with Morrison who took the ball on in a strong burst and with the Munster defence exposed, he offloaded for the supporting Jackson to dive over the try-line and score.
Jackson had to go off after damaging his shoulder. His fellow replacement Mark McMillan took over the kicking duties and nailed the conversion from left of the posts.
Try as they might, Munster could find no way back and Glasgow's 'Killer Bees' back row unit of Kelly Brown, Johnnie Beattie and John Barclay deservedly took the plaudits afterwards for an excellent collective display.
McMillan pushed a late penalty away from the target but it did not matter. Munster were out of ideas and out of time.
|Glasgow Warriors Score Card|
|Munster Rugby Score Card|