However, Colin Gregor's conversion attempt sailed wide and, in the end, tries from Peter Stringer, Barry Murphy and Doug Howlett were enough to give Munster the points which move them back to the Magners League's summit.
More than 19,000 spectators turned up to see Munster begin a new era at their redeveloped Limerick ground and they did not have long to wait for the first score.
There were just 83 seconds on the clock when Stringer pounced for the opening try.
Bernardo Stortoni ill-advisedly took a quick line-out throw, passing behind his try-line to John Beattie.
But the Glasgow number eight dropped the greasy ball and the ever-alert Stringer was in like a flash to touch down.
Television match official Brian Fitzgerald confirmed the grounding and with Ronan O'Gara quickly converting, Munster were up and running.
Gregor, a nemesis of Munster's in the past, missed a tricky penalty chance to reply.
Filling in for the injured Dan Parks, Gregor gradually grew into his role and he found his kicking boots towards the end of the half.
O'Gara nudged a penalty from distance through the posts for a 10-0 lead, with Munster pressing well through Doug Howlett and Keith Earls.
Stortoni was energetic as ever for Glasgow, while scrum-half Mark McMillan box-kicked well and linked smoothly with his pack.
The Glasgow forwards gnarled away at the breakdown and forced a 32nd-minute penalty which Gregor landed for a 10-6 interval deficit.
A nasty collision with Earls cut short Thom Evans' night but his brother Max launched a fine counter-attack, on the resumption, to show Glasgow's intent.
Try-scoring chances were at a premium and when Gregor missed two penalties, either side of half-time, Munster took their cue.
O'Gara notched his second penalty and in the 54th minute, Murphy got over in the left corner after a barging run from Earls and a dinked kick from Rua Tipoki.
The Irishmen were never out of sight though and two Gregor kicks cut the gap back to 18-12 in the final quarter.
A move straight off the training ground allowed Munster to reassume control - a line-out tap-down and a string of passes sent Howlett over for his fourth try of the campaign.
Yet Munster's push for a bonus point score never really materialised and gutsy Glasgow had the final say when Stortoni and Max Evans combined to put O'Hare through on the left.