The Irish giants moved to fifth place on the table courtesy of the victory, while the Lions had already confirmed their quarterfinal berth thanks to Glasgow beating Ulster.
Lions started well in hostile territory, piling the pressure on the hosts, but it was Munster who crossed the whitewash first when Evan OÃonnell bashed over from close range.
Fullback Quan Horn got the visitors on the scoreboard thanks to a perfectly timed intercept and a 70m run to score in splendid isolation under the poles.
With the Lions on attack, Munster would earn two yellow cards in quick succession. First, Andrew Smith stuck out his hand to prevent a pass, then Sean OâBrien did the exact same thing on the other side of the field minutes later, reducing them to 13 men.
It looked as though they would get away with the infringements, but the Lions eventually capitalised, and Kelly Mpeku ran in an easy score.
But Munster fought hard with 14 on the park and nuggety number nine Craig Casey sniped over for a crucial try, sending them down the tunnel at 17-14.
In the 54th minute, after multiple waves of attack, Munster's Tom Ahern crashed over and JJ Hanrahan's conversion took the lead out to ten points.
Five minutes later, Chris Smith kept the Lions in touch with a penalty, which ended up being the final points of the match.
There were distasteful scenes later on. Diarmuid Barron accused one of the Lions players of spitting in his face, but TMO Stefano Penne found no evidence. The Lions camped in the Munster half for the remainder of the match, but couldn't land the knockout punch.