The champions have yet to concede a try in this season’s competition but two more yellow cards — on top of three in the opening day win over the Dragons — will be a cause for some concern for coach Tony McGahan.
But once more Munster made light of their absent stars and while Glasgow made a game of it early on, the Reds got on top and dominated the game.
There was little between the sides during the opening half but Munster came good before the break to push 16-6 ahead at the interval.
Their chronic trouble with yellow cards manifested itself as early as the 13th minute when Niall Ronan was binned for killing the ball after Danny Barnes had done well to haul down Rob Dewey with the line in sight.
Duncan Weir added the penalty in front of the posts but that was the only score Munster conceded when they were down a man.
Earlier, Ian Keatley and Weir had traded penalties, while Simon Zebo needed to be sharp to deny his opposite number Federico Aramburu in the right corner after early Glasgow pressure.
Glasgow lost a man to a yellow card when Chris Fusaro followed his opposite openside flanker to the bin for not rolling away.
Keatley added the penalty to tie the sides at 6-6 after 22 minutes but Munster, similar to Glasgow, failed to make their extra man count on the scoreboard.
Weir missed a penalty from the right after Johne Murphy, who was superb under the dropping ball, was penalised for a scuffle with Weir.
But Munster stepped up a gear before the break with James Coughlan leading the way up front.
Keatley edged them in front with a penalty from inside his own half and then just before the break a superb run from Barnes saw Munster twice tap penalties inside the 22 before Ronan, who had scored in three of his last four visits to Firhill including a hat-trick, squeezed over, with Keatley adding the extras.
Munster all but decided the issue five minutes after the restart. Ronan and Peter Stringer stretched the home defence before Lifeimi Mafi cut a superb line and fed Simon Zebo to score.
Keatley added the points and while Weir hit a couple of penalties, Munster were never threatened, even when Billy Holland was binned 11 minutes from time for killing the ball.
Scorers for Glasgow Warriors: Pens: Weir 4.
Scorers for Munster: Tries: Ronan, Zebo. Cons: Keatley 2. Pens: Keatley 3.
GLASGOW WARRIORS: S Hogg; F Aramburu, R Dewey, T Nathan, C Shaw; D Weir, H Pyrgos; R Grant, P MacArthur, M Cusack; T Ryder, N Campbell; R Harley, C Fusaro, R Wilson.
Replacements: J Eddie for Campbell 46; C Gregor for Pyrgos 46; E Kalman for Cusack 53; P Horne for Dewey 57; F Gillies for MacArthur 72; R Pitman for Wilson 72; S Wight for Weir 75; G Reid for Grant 76.
MUNSTER: J Murphy; D Howlett, D Barnes, L Mafi, S Zebo; I Keatley, P Stringer; W du Preez, D Varley, J Hayes; B Holland, M O’Driscoll; P O’Mahony, N Ronan, J Coughlan.
Replacements: S Archer for Hayes 59; T O’Donnell for Ronan 59; M Horan for du Preez 62; D Williams for Stringer 65; D Fogarty for Varley 67; T Gleeson for Zebo 73; D Foley for O’Mahony 73; S Deasy for Keatley 75.
Referee: D Phillips (IRFU).