Impressive backrower Anthony Foley scored the Irish province's first try and produced a deft chip for fullback Christian Cullen to give Munster a 17-7 lead at the break.
Ospreys winger Shane Williams had silenced the home crowd with an early try, but it was to be his side's last as they bowed out of Cup contention.
Munster need a win over NEC Harlequins at Twickenham next weekend to ensure playoff qualification.
Munster scrum-half and man of the match Peter Stringer admitted his side had to fight all the way for their victory over the Welsh region.
"We knew it would be difficult," the Test star said. "They're a side that really come at us and make it hard for us.
"We managed to get a couple of scores just before halftime which gave us the confidence to go on with it."
Munster (17) 20: Tries: Foley, Cullen Cons: Burke 2 Pens: Burke 2
Ospreys: (7) 10: Tries: Williams Cons: Henson Pens: Henson
C Cullen; M Lawlor, S Payne, M Mullins, A Horgan; P Burke, P Stringer; M Horan, F Sheahan, J Hayes, D O'Callaghan, P O'Connell, A Quinlan, D Leamy, A Foley (capt).
Replacements: G McIlwham, J Flannery, T Hogan, J Williams, M Prendergast, J Holland, J Storey.
A Durston; S Terblanche, S Parker, G Henson, S Williams; M Jones, J Spice; D Jones, B Williams (capt), A Millward, B Cockbain, J Thomas, J Bater, R Pugh, R Jones.
Replacements: R Hibbard, P James, A Jones, A Newman, A Lloyd, D Bishop, E Seveali'i.
Referee: Chris White (England). Att: 13,200.