Tony McGahan's men began their title defence in style with a 20-12 defeat of the Dragons last week and continued to impress against the Warriors with Niall Ronan crossing for the game's other try on the stroke of half-time.
And despite missing out on a try bonus point for the second week running, 13 points from the boot of Ian Keatley ensured Munster were always in control of the game.
After Keatley and Duncan Weir exchanged penalties Glasgow were handed a man advantage when Munster flanker Ronan was sent to the sin-bin for illegally impeding home No.9 Henry Pyrgos' work at the scrum.
Weir slotted the resulting penalty but the scores and the sides were level soon after when Ronan's opposite number Chris Fusaro was sent to the bin and Keatley threaded the ball through the posts.
Glasgow almost edged back ahead when Weir's drop goal attempt struck the upright and though veteran scrum-half Peter Stringer fumbled the restart the hosts failed to build on the territory.
Keatley was also left frustrated on 30 minutes when he wasted a chance to add a further three points to the scoreboard but Munster were let off the hook again when Johne Murphy was penalised for a dangerous tackle on Weir - only for the 20-year-old to fail to punish him with the penalty.
Keatley rediscovered his kicking boots on 35 minutes when he landed a huge penalty from inside his own half.
After defending manfully for 40 minutes Glasgow were undone in time added on when a quick tap penalty allowed the returning Ronan to scamper over the line, with Keatley converting to send Munster in at the break 16-6 up.
All talk in the Glasgow dressing room must have revolved around striking back early but instead it was Munster who extended their lead shortly after the break.
From a maul the wily Stringer released Lifeimi Mafi at full speed and despite being held up short of the line the Tongan centre popped the ball up for Zebo to finish the move, which Keatley again converted.
Weir responded almost instantly with a penalty on 47 minutes and reduced the gap by a further three points four minutes later but that was as far as the Warriors managed to get.
|Glasgow Warriors Score Card|
|Munster Rugby Score Card|