Four penalties and a drop goal by fly half Jeremy Manning put them 15-0 up before the Ospreys Shaun Connor scurried over for a try, which he converted.
Munster regained their 15-point lead by half-time with No.8 James Coughlan forcing his way over. Ospreys winger Jonny Vaughton darted over for a try and although they closed the gap, Munster held on for the win.
Despite most of their first-choice players being on international duty, Munster raced into that early lead thanks to the kicking of 21-year-old New Zealand born Manning.
The Ospreys hit back with former All Blacks scrum-half Justin Marshall taking a quick tap and offloading to Jason Spice, who sent Connor in for a well-worked try. Munster responded with their only touchdown: Coughlan ploughing over on the end of a five-metre scrum for his first provincial try.
The Ospreys got back within range just five minutes into the second half. A sweet inside pass from Tal Selley sent winger Vaughton through for his first try of the league campaign.
Yellow cards for Spice and Federico Pucciariello - the Munster prop was left bloodied after a clash with Brent Cockbain - disrupted the pattern of the game, but Manning cooled matters with his fifth penalty.
The final quarter saw Connor kick two more penalties but they were not enough to prevent a nervy Munster holding on for victory.
Munster (22) 25
Pens: Manning (5)
Drop goal: Manning
Ospreys (7) 20
Tries: Connor, Vaughton
Cons: Connor (2)
Pens: Connor (2)
Munster: Payne, Horgan, Mafi, Halstead, Dowling, Manning, O'Leary, D Hurley, Kyriacou, Pucciariello, O'Driscoll, Wyatt, Quinlan, McGann, Coughlan
Replacements: Roche, Buckley, D Ryan, O'Sullivan, O'Meara, Hickey, Murphy
Ospreys: Terblanche, Vaughton, Selley, Spice, Walker, Connor, Marshall, James, B Williams, Millward, Powell, Bateman, Lloyd, Tandy, Tiatia
Replacements: Bennett, Griffiths, Cockbain, Beech, Pugh, Spratt, Byrne
Referee: Ian Heard (SRU).