Niall Ronan and Simon Zebo crossed for tries either side of half-time, Ian Keatley converted both scores and adding three penalties for a 13-point personal haul.
Glasgow lacked imagination throughout, with only four Duncan Weir penalties to show for their efforts as Munster followed Ulster in inflicting defeat on Sean Lineen's inexperienced side.
Glasgow came close in the opening minute when Freddie Aramburo was inches short of a crafty Weir chip but from the scrum, Munster pinned Glasgow well back into their own half and kept the field position until the home side offended, allowing Keatley to open the scoring with a simple penalty.
Munster returned the favour from the restart and Weir levelled the scores, and Henry Pyrgos then came close to the first try only to be pulled down five metres short after collecting his own chip ahead.
Troy Nathan was the next Glasgow attacker to ask the question of the Munster defence, earning a penalty from which Weir eased Glasgow ahead. Keatley levelled the scores, though, and then a long-range attempt by the Munster number 10 took them ahead.
The game seemed to be meandering towards the break when suddenly Munster upped the pace. Danny Barnes burst past Rob Dewey and although the Glasgow scramble defence held for a couple of minutes, the pressure told and Ronan was driven over. Keatley added the conversion to take Munster in 16-6 ahead.
The second half suited the Munster pack, who ran the game with the home side offering very little.
The sharpest move came from Munster in the 45th minute, Zebo getting on the end of a sweeping move to grab the second try for the visitors.
Weir reduced the margin with two penalties in the 47th and 50th minutes but the home side could make little of the limited ball they won.
Munster flanker Peter O'Mahoney, with Ronan at his elbow, were hard for the Glasgow backs to handle, Mick O'Driscoll and John Hayes took control of the game up front and only when James Eddie came on and Rob Harkey moved to lock did Glasgow achieve any real impetus, by which point it was too little too late.
Munster were never under any threat for the last half-hour and collected their second win in the competition with some ease, while Glasgow have the problem of allying penetration and drive to what can only be described at present as youthful enthusiasm.
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