In the opening half Ospreys number 10 Dan Biggar kicked two out of three penalty chances to give the visitors six points. Doug Howlett scored the first try of the game after ten minutes with O'Gara adding a penalty just before the break to give Munster a marginal two point lead at halftime, 8-6.
On the return Tommy Bowe grabbed an intercept try running the length of the field to score under the posts moving Ospreys five points ahead before Munster responded with tries from David Wallace and Johne Murphy, O'Gara converting both, 22-13 after 63 minutes.
Ospreys claimed a losing bonus point when Biggar added his third penalty to give a final scoreline of 22-16.
Tony McGahan after the win "I thought we showed great intent and great endeavour today. The pressure is really on the home sides and you can't afford not to get your four points."
Mick O'Driscoll added "Ospreys are one of the top teams around, they're very hard, they're very dogged and physical around the park. They're a good side and they came over here with the belief they could win and we're going to go over there with the belief to win. We hope going into next week we can take the step up and get the four points."
Munster: P Warwick; D Howlett, K Earls, S Tuitupou, J Murphy; R O'Gara, T O'Leary; W du Preez, D Varley, T Buckley; D O'Callaghan, M O'Driscoll; J Coughlan, D Wallace, D Leamy capt. Replacements: M Sherry, D Hurley, J Hayes, P O'Connell, A Quinlan, P Stringer, L Mafi, D Hurley.
Ospreys: Barry Davies; Tommy Bowe, Andrew Bishop, James Hook, Richard Fussell; Dan Biggar, Mike Phillips; Paul James, Richard Hibbard, Adam Jones; Ryan Jones, Alun Wyn Jones; Jerry Collins, Marty Holah, Jonathan Thomas. Replacements: Mefin Davies, Duncan Jones, Craig Mitchell, Ian Gough, Justin Tupuric, Jamie Nutbrown, Sonny Parker, Tom Prydie