Despite outscoring their hosts by two tries to one, Munster's season ended in deep frustration as they fell at the league's penultimate hurdle - a double disappointment after their Heineken Cup semi-final exit last month.
Captain Damien Varley and Sean Dougall, arguably Munster's most impressive player on the night, scored tries in either half at a packed Scotstoun.
But the visitors were left to rue the three penalties which Finn Russell landed to give Glasgow a 9-7 interval lead, and the young out-half followed up by converting Gordon Reid's 46th-minute try.
That left Munster nine points adrift and although Dougall crashed over soon after and Ian Keatley added a 66th minute penalty, the Scots held on in determined fashion to set up a title decider against either Leinster or Ulster.
There were great scenes of jubilation at the finish as the Warriors, having lost five previous semi-finals in all competitions, finally reached their first league decider.
It was a gut-wrenching way for Rob Penney's Munster coaching tenure to come to an end, and it leaves the province to reflect on the fact that they have only won one of their last nine semi-finals, both domestic and European (the lone success was against the Ospreys in the league's last-four at Thomond Park in 2011).
These two hugely committed sides had opportunities to attack during a frantic first five minutes, with the league's Young Player of the Year Jonny Gray and Tommy Seymour both making good ground for Glasgow.
David Kilcoyne and James Coughlan drove Munster on up front with Felix Jones, who unfortunately had to go off injured before half-time, getting an early chance to stretch his legs.
Good work at the breakdown from flanker Dougall forced a penalty and got Munster into scoring range. The visitors used the ensuing lineout to send James Downey crashing up through the middle and the platform was laid for the game's opening try.
As Keith Earls and Alex Dunbar scuffled off the ball, the Munster pack went through a series of pick and goes with a final one seeing hooker Varley barge over from just inches out. TMO Carlo Damasco confirmed the grounding and Keatley swept over a fine conversion from the left.
The otherwise excellent Russell missed a kickable chance to respond after Josh Strauss gave the Warriors some momentum over halfway.
But Glasgow began to exert some pressure as they continually got over the gain-line and after Earls infringed at a ruck and fired-up captain Al Kellock clattered into Paul O'Connell, Russell took the three points on offer this time.
Kellock was fortunate to get away with a neck-high challenge on O'Connell soon after, the ferocity and physicality of these Celtic rivals leading to some intense passages of play and bone-crunching hits.
A dollop of defensive grit from Munster yielded turnover ball and try scorer Varley showed good pace on the right touchline as the tit-for-tat exchanges continued.
Number 10 Russell was beginning to influence proceedings with ball in hand and Sean Maitland was put into rare space on the left, however once more Munster's accurate breakdown work was rewarded with a relieving penalty.
A terrific break from Dougall, who profited from a Conor Murray dummy, should have led to a second Munster try on the half hour but a stretching Simon Zebo was denied by three covering defenders.
Both sides had to cope with injuries with Casey Laulala and Strauss forced off and Jones following them, however Glasgow coped well without their South African enforcer and Russell made it a one-point game with a second successful penalty.
Munster fell foul of referee Marius Mitrea's whistle again when a marginal scrum call went against BJ Botha and Russell booted Glasgow in front for the first time.
After a well-earned break, the teams resumed with the Scots in the ascendancy. A Russell touchfinder led to a Munster error from a quickly-taken lineout and Gregor Townsend's men sensed a try.
Chris Cusiter did well to tidy up scrappy possession from a five-metre scrum and as Glasgow maintained the momentum through a number of forward drives, replacement prop Reid drove over in the left corner with Russell converting with aplomb.
Munster were quick to respond, again using big centre Downey to bulldoze up through the middle with young Russell the target.
The red tide swept ever closer to the try-line and O'Connell popped the ball to the right from a close-in ruck for Dougall to dive over and score.
Keatley failed to add the extras, a missed kick he was left to rue come the final whistle. Despite that, the Dubliner deserves plenty of credit for his efforts in keeping Munster in contention, with Jones' injury seeing Keatley slot in at full-back with JJ Hanrahan taking the reins at out-half.
Both defences tightened up thereafter with Downey winning a ruck decision for Munster as they swiftly turned defence into attack. However, Reid stepped up for the hosts when doing likewise at the other end of the pitch.
The tension increased entering the final quarter as Sean Maitland hacked through into the Munster 22, the retreating Zebo was unable to grasp the bouncing ball and Keatley came to his side's rescue by kicking it into touch.
Glasgow then lost field position through a crooked lineout and scrum penalty and it was Munster's turn to attack, drawing a penalty from big Fijian Leone Nakawara who failed to release Earls on the deck.
Keatley's effort off the kicking tee crept inside the left hand upright and Glasgow's lead was down to 16-15 with a quarter of an hour left.
Apart from the penalty concession, Nakawara and fellow Fijian Niko Matawalu both made quite an impact off the bench with some important breaks and offloads in the closing stages.
Munster looked the more composed team as they went through the phases, however Glasgow continued to threaten off limited ball with replacement scrum half Matawalu attacking the fringes of rucks.
The record 10,000-strong crowd willed Seymour over the line when he intercepted a pass just inside the Munster half but Zebo raced back to foil the former Ulster winger.
Earls and Andrew Conway offered themselves as threats out wide as Munster, who dominated possession in the dying minutes, desperately tried to create an opening.
Credit to Glasgow's disciplined defence, they kept Munster near the halfway line and out of scoring range as the province lacked the penetration to truly test the Warriors' mettle.
The joy was obvious for Townsend and his players at the final whistle. Noted as the form team entering the play-offs, this was a record ninth straight win for Glasgow who will face Irish opposition again in the May 31 final.