Munster made it six wins out of six in Pro14 Conference B as Glasgow were consigned to a fifth defeat.
Billy Holland and Fineen Wycherley crossed for a 12-8 Munster lead, Glenn Bryce grounding for Warriors.
Ben Healy added a penalty to his earlier conversion but team-mate Holland was then sin-binned.
Grant Stewart got the hosts' second try but Glasgow's Ryan Wilson was yellow carded before Gavin Coombes and Jean Kleyn sealed the visitors' bonus point.
The one thing that can be said of this one is that it was fiery. It nearly always is when these sides meet. There were scuffles to begin with and they got worse later on. At one point, both captains were in the bin.
A second half melee could have brought a red, or two, as a few punches appeared to land. Referee Adam Jones struggled to keep control, not just in dealing with the aggravation but in general play. He will need a lie down after this.
Wilson was at the heart of the aggravation, both sinned against and sinning. He's Glasgow's totem and the man Munster dislike most. There's history, as they say. He's a marked man who revels in his notoriety with the men in red.
Glasgow, shorn of 22 players and with only win this season, were desperate to get their season back on track and Wilson was more determined than anybody. Glasgow got off to a grim start, though. It was bad enough that they lost Nick Grigg, only just released back to them by Scotland, early on after the centre failed to return from a HIA, but they also shipped a try inside nine minutes.
The Munster lineout maul was a serious weapon in the foul conditions at Scotstoun, a night of wind and rain and errors by the bucket-load. Glasgow coughed up a lineout and then got done on the floor and from the penalty Munster went to touch. At the second attempt they barrelled over, the veteran Holland touching down.
The response was swift and impressive. Tommy Seymour found a gap and sprinted through it, then flung out a pass that hit grass before being gobbled up Robbie Nairn. The wing did wonderfully to brush off four Munster defenders before getting a pass away to Bryce who scored in the corner.
That offload looked like it went forward, but Glasgow got away with it. They hit the front when Brandon Thomson, on for Grigg, boomed over a penalty from the halfway line. Thomson had the wind at his back but it was still a thumping strike.
Another bit of misfortune befell Glasgow when they lost Seymour to another brain injury assessment on the half-hour. He was off for only a minute when Munster scored their second try. It was another close-range maul, another unstoppable drive, Wycherley getting on the end of it this time. Healy missed the conversion but the visitors were back in front.
The knock-ons, ropey kicks, lost lineouts and penalties flowed. Exhilarating, it was not. Healy put Munster further ahead early in the second half, either side of kicking dead twice. The second error was almost humorous, the wind taking his clearance kick from his own 5m line all the way over Glasgow's line down the other end of Scotstoun.
That was the cue for a sustained battering of the Munster line. They had a scrum, then a maul, then penalties, then four shots at driving over from a lineout. Eventually, they cracked it when Stewart blasted over. Thomson missed the conversion, but Glasgow had some encouragement and one extra man.
In their desperate efforts to keep the Warriors out, Holland got binned. Munster were a touch fortunate that they did not have two men in the bin instead of one.
Seven minutes after Holland was yellow-carded, his counterpart Wilson went the same way. The narkiness was on the rise and it kicked off when Wilson went in dangerously on the influential Craig Casey, the Munster scrum-half. Casey was on the floor at the time. The afters led to players piling in on both sides.
Munster's superior muscle saw it out comfortably, Coombes driving over with 10 minutes left to play followed just before full-time by Kleyn.
Glasgow's season gets more troubled by the week.
Glasgow Warriors head coach Danny Wilson: "Not great conditions at all and that leans towards a power game that we struggled to deal with from Munster. At times our game management let us down.
"On a night like like tonight, you've really got to be on top of your discipline. A lack of discipline really hurt us towards the end of the game. We'll patch up and we'll keep working hard with this group. We'll keep demanding our minimum standard and it'll turn."
Glasgow: Bryce, Seymour, Grigg, Fergusson, Nairn, P Horne, Kennedy, Seiuli, Stewart, Pieretto, Bean, Harley, Wilson, Gordon, Ioane.
Replacements: Matawalu for Seymour (29), Thomson for Grigg (8), Allan for Seiuli (51), Rae for Pieretto (51), Bain for Bean (71), Lokotui for Ioane (52). Not Used: Matthews, Korteweg. Sin Bin: Wilson (68).
Munster: Haley, Nash, R Scannell, de Allende, Gallagher, Healy, Casey, J Cronin, O'Byrne, Archer, Kleyn, Holland, F Wycherley, O'Sullivan, G Coombes.
Replacements: Goggin for Gallagher (70), Hanrahan for Healy (70), McCarthy for Casey (77), J Wycherley for J Cronin (67), Marshall for O'Byrne (61), Knox for Archer (68), O'Donoghue for F Wycherley (61), O'Donnell for O'Sullivan (67). Sin Bin: Holland (61).