Domingo Miotti added a drop-goal on 44 minutes for a 31-0 advantage before the Munster comeback began on 53 minutes.
Munster salvaged a four-try bonus-point on a very disappointing night at Thomond Park on Saturday with Glasgow Warriors claiming a deserved victory.
The visitors led 31-0 after a clinical opening 44 minutes that saw them score four converted tries and kick a drop-goal with Munster sloppy in possession. Whenever the province looked to string phases together, knock-ons stymied any chance of gaining momentum.
Despite having very little to cheer about, the home support stayed behind the team and were rewarded with four tries in the final 36 minutes as Gavin Coombes, Craig Casey, Josh Wycherley and Calvin Nash, all touched down to salvage something out of the game.
Jack Crowley was unable to add the touchline conversion as Munster managed to eke out a four-try bonus-point and stay fifth in the table with two rounds to go.