Perhaps the decisive score came just before the break when Munster turned over possession deep in the Ospreys half and the home side raced away for Kahn Fotuali'i try to leave Ospreys leading 23-10.
And after that it was all downhill as the home side as Hanno Dirksen and Andrew Bishop added tries to leave Ospreys 38-10 in front with 17 minutes remaining.
Replacement Rhys Webb added another with ten minutes to go.
Ospreys: R Fussell; H Dirksen, A Bishop, A Beck, S Williams; D Biggar, K Fotuaili'i; P James, R Hibbard, A Jones, A Wyn Jones, I Evans, R Jones, J Tipuric, J Bearman. Replacements: S Baldwin, R Bevington, A Jarvis, J King, T Smith, R Webb, M Morgan, T Isaacs.
Munster: J Murphy; I Dineen, K Earls, L Mafi, S Zebo; I Keatley, C Murray; W du Preez, M Sherry, B Botha, D O'Callaghan, M O'Driscoll, D Ryan, T O'Donnell, P O'Mahony. Replacements: D Fogarty, D Kilcoyne, S Archer, Dave OCallaghan, P Butler, T OLeary, R OGara, D Barnes.
Referee: A Rolland