Centre Lifeimi Mafi scored one try and set up another as Munster avoided a third straight defeat to leap-frog the Ospreys to go top of the Magners League.
Home outside-half James Hook did kick seven penalties to earn his side a losing bonus point in a 25-21 loss.
As the half-time score of 11-9 suggested the first half was a nip and tuck affair involving the top two with such one point separating the teams.
But Munster were handed a major boost when Mafi went over in the right corner for an unconverted try, a score that was awarded on referral to the TV match official Nigel Whitehouse.
Hook got the Ospreys on the scoreboard almost straight away with a penalty goal after Paul Wallace came in from the side of a ruck, but it was cancelled out three minutes later with a Paul Warwick penalty from a scrum infringement.
The Ospreys, who welcomed back Shane Williams from a shoulder injury, had their moments, especially when Andrew Bishop broke through two tackles, but kept losing the ball or being pinned back in their own half with penalty kicks to touch.
A fine Hook penalty from 45 metres following another Wallace infringement was again cancelled out by Wallace.
The Ospreys had their best chance of a try when Jonny Vaughton, on his 50th appearance, dived in at the left corner but a try was ruled out for a foot in touch.
After 38 minutes Munster were dealt a blow. Already without Ronan O'Gara the Irish Province lost Warwick with a facial injury.
And the home side had the final say with an injury-time penalty for Hook to cut the Munster deficit to two points.
Two Hook penalties - one from halfway - at the start of the second half gave the Ospreys the lead for the first time.
But the Ospreys' advantage was cut to a point on 52 minutes when replacement outside-half Conan Doyle converted a penalty from in front of the posts.
A quick tap penalty from Shane Williams brought the crowd alive as they sensed the ospreys first try a score was ruled out when Ian Dowling killed the ball in front of his own posts, earning him a yellow card.
But the Ospreys had the consolation of a sixth penalty from Hook to extend their lead to 18-14.
Just after the hour mark Munster were back to within a point of the lead with a second Doyle penalty after Ospreys flanker Steve Tandy was sin-binned for a professional foul.
And one less in their pack had an effect as scrum-half Thomas O'Leary scored eight unanswered points. First he was put over for a try created by Mafi before putting over a penalty.
Hook did put over his seventh penalty after 76 minutes to keep in the Ospreys touch but Munster, who used three players at outside-half, did enough to close out the game.
Peter O'Mahony was named man of the match against England last month
21 April 2017, 7:22pm
Peter O'Mahony's performance in the RBS 6 Nations finale for Ireland against England was crucial to his selection for the British & Irish Lions on Wednesday, Ireland and Lions defence coach Andy Farrell has revealed.