Fly-half JJ Hanrahan scored all of Munster's points as they defeated league leaders Glasgow 13-6 at Scotstoun Stadium.
The Warriors went into the break 6-3 ahead through Duncan Weir's two penalties, with the visitors' response coming through Hanrahan.
But the Irish province dominated the initial part of the second half and their fly-half scored a try before adding a three-pointer to secure a vital win.
Glasgow's campaign was disrupted two weeks ago when they were thrashed 51-28 by Toulon in Europe. However, they responded well to that setback by overcoming Exeter Chiefs 20-16 in the second round of the Heineken Cup.
Buoyed by their previous result, they were out of the blocks early against Munster as Weir kicked a penalty after just two minutes.
The fly-half then had a chance to extend the lead for Gregor Townsend's men, but his effort missed, and the visitors capitalised as Hanrahan levelled matters with a three-pointer of his own.
Both teams were struggling to put consistent phases of play together, but the Warriors' fly-half was again on target from the tee when the Irish province infringed.
Although the visitors pressed late in the half, Glasgow held on and went into the break 6-3 ahead. Munster started the second period in the ascendancy once more and a try from their stand-off was just reward for the pressure they had exerted.
Hanrahan then extended the advantage for Rob Penney's side with a penalty and, despite late Glasgow attacks, they defended resiliently throughout to take the spoils.
Pens: Weir (2)
Yellow Card: Welsh
Pens: Hanrahan (2)
Yellow Cards: Cronin, Kilcoyne
Glasgow Warriors: 15 Sean Maitland, 14 Tommy Seymour, 13 Byron McGuigan, 12 Sean Lamont, 11 DTH van der Merwe, 10 Duncan Weir, 9 Chris Cusiter (c), 8 Josh Strauss, 7 Tyrone Holmes, 6 Rob Harley, 5 Jonny Gray, 4 Tim Swinson, 3 Moray Low, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Dougie Hall, 17 Jerry Yanuyanutawa, 18 Jon Welsh, 19 Tom Ryder, 20 Chris Fusaro, 21 Niko Matawalu, 22 Ruaridh Jackson, 23 Mark Bennett.
Munster: 15 Johne Murphy, 14 Andrew Conway, 13 Keith Earls, 12 Ivan Dineen, 11 Ronan O'Mahony, 10 JJ Hanrahan, 9 Conor Murray, 8 CJ Stander. 7 Sean Dougall, 6 Peter O'Mahony (capt), 5 Paul O'Connell, 4 Donncha O'Callaghan, 3 Stephen Archer, 2 Mike Sherry, 1 James Cronin.
Replacements: 16 Damien Varley, 17 David Kilcoyne, 18 BJ Botha, 19 Billy Holland, 20 James Coughlan, 21 Cathal Sheridan, 22 James Downey, 23 Casey Laulala.
Referee: Ian Davies (Wales)
Assistant referees: David Changleng, Bob Nevins (both Scotland)
Television match official: Jim Yuille (Scotland)