Glasgow deservedly came out on top in this vital RaboDirect PRO12 battle as they secured a play-off spot among the top four sides courtesy of a 35-17 victory.
They were made to work hard by the Welsh side but shrugged off place-kick misses by stand-off Duncan Weir, and a later injury to the player that saw him carried off on a stretcher, to score the bonus point win that ensures a top-four finish.
They ran in first-half tries through prop Ryan Grant (two) and winger Sean Maitland before scrum half Niko Matawalu grabbed the fourth in the second half and DTH van der Merwe made himself the top Glasgow try scorer with a counter to close the game.
Weir succeeded with two conversions and a penalty plus Peter Horne goaled a penalty.
Cai Griffiths and Sam Lewis scored tries for Ospreys, while Dan Biggar kicked two conversions and a penalty.