Two second half tries from Richard Fussell and Rhys Webb consigned Munster to a 19-13 defeat in the Liberty Stadium.
And to add further to what was a disappointing night, try scorer Doug Howlett
was helped off in the closing stages with what management say looks to be an Achilles injury.
Howlett looked particularly lively whenever he was on the ball and up to the time of his try Ian Keatley and Matthew Morgan had swopped three penalties apiece, each on the mark just once to leave the sides tied three points apiece.
Munster's score came after Simon Zebo had made good progress down the left wing before play switched right and Howlett was quickest to react when a Will Chambers kick thru ricocheted off an Ospreys defender over for Howlett to get the touchdown and send his side in 10-6 to the good at the break.
Within less than 10 minutes of the restart the whole landscape had changed thanks to two tries from Fussell and Webb but Munster kept themselves in contention with a penalty from Ronan O'Gara who had entered the fray in the 50th minute.
And in the closing minutes as Munster chased 19-13 lead they forced a series of five metre scrums that they shunted back time and again. However, on the last put-in, with a penalty try surely in the offing, referee Peter Allan, penalised the BJ Botha to allow Ospreys lift the siege.
Munster: D Hurley; D Howlett, W Chambers, D Barnes, S Zebo; I Keatley, T O'Leary; M Horan, D Varley, BJ Botha; D O'Callaghan, D Ryan; D Leamy, N Ronan, P O'Mahony capt. Replacements: D Fogarty, W du Preez, S Archer, P O'Connell, J Coughlan, C Murray, R O'Gara, J Murphy.
Ospreys: B Davies; T Bowe, A Bishop, A Beck, R Fussell; M Morgan, R Webb; D Jones, R Hibbard, A Jarvis; I Gough, J Thomas; T Smith capt, J King, J Bearman. Replacements: M Davies, C Griffiths, J Rees, G Stowers, S Lewis, T Isaacs, S Parker, H Dirksen.
Referee: Peter Allan.