Sean Dougall, Simon Zebo and James Downey were the try-scorers as Rob Penney's side won away at Ospreys for the first time since 2011.
Munster have now won 14 out of their last 15 games in all competitions and lead the PRO12 by two points from second-placed Leinster.
After the game, Head Coach Penney said: "We are really pleased to get a win - Ospreys are a talented group and have been there or thereabouts all season. The Liberty Stadium is a difficult place to come. A number of our boys have not won here before so it's a wee bit of a special one."
Munster return to Wales on Saturday to face Scarlets with a 6:30pm kick-off at Parc y Scarlets.