It looked pretty good for the Welshmen as they lead by 12 points at the break. Outside half Steffan Jones went over for a try, with centre Ross Wardle adding another in the second-half, while full-back Tom Prydie finished the game with 17 points via five penalties and a conversion.
Jones also kicked a neat drop goal on the stroke of half-tiime as Munster walked to the changing room in trouble with only a try from number eight Paddy Butler to show for their efforts.
But tries from wing Ronan O'Mahony, replacement CJ Stander and wing Johne Murphy plus two Ian Keatley conversions after the interval put them right back in it before they succumbed despite picking up two bonus points, one for getting four tries and the other for being within seven points of the winners.
Glasgow deservedly came out on top in their vital battle against the Ospreys as they secured a play-off spot among the top four sides courtesy of a 35-17 victory.
They were made to work hard by the Welsh side but shrugged off place-kick misses by stand-off Duncan Weir, and a later injury to the player that saw him carried off on a stretcher, to score the bonus point win that ensures a top-four finish.
They ran in first-half tries through prop Ryan Grant (two) and winger Sean Maitland before scrum half Niko Matawalu grabbed the fourth in the second half and DTH van der Merwe made himself the top Glasgow try scorer with a counter to close the game.
Edinburgh were unable to hold on to an early 10-point advantage as Benetton Treviso hit back to take a 301- victory in their clash in Italy.
Even the loss of Edoardo Gori and Ignacio Fernandez-Rouyet to the yellow cards in the final seven minutes failed to slow Benetton, who climb up to seventh on 43 points after competing the double over the opponents this season. Edinburgh, meanwhile, are 10th with 32 points.
Stuart Olding was in sensational form as leaders Ulster beat Connacht 34-18 after a high-scoring first half.
The scoring dried up in a hard-fought second period, a Miah Nikora penalty getting Connacht closer, although the league leaders showed their class late on with Tommy Bowe's bonus point try and a fifth from Jared Payne.