Ospreys (24) 34
Tries: Tiatia, Owen, Nutbrown Cons: Hook 2 Pens:Hook 5
Glasgow (15) 23
Tries: Stortoni, Fa'atau 2 Cons: Jackson Pens:Jackson 2
Ospreys try-scorer Gareth Owen tangles with Bernardo Stortoni
The Ospreys overcame Glasgow Warriors at the Liberty Stadium to move up to third in the Magners League.
Tries by Filo Tiatia and Gareth Owen helped the hosts into a 24-15 half-time lead with Bernardo Stortoni and Lome Fa'atau crossing the line for Glasgow.
Jamie Nutbrown's try put the Ospreys firmly in command but the home side could not notch the score that would have guaranteed them a bonus point.
Fa'atau sped away to claim Glasgow's third try late on.
The Ospreys, who announced the signing of former All Black Jerry Collins before kick-off, overtake Edinburgh in the standings while the Warriors remain seventh.
Glasgow started brightly and grabbed the opening try when Fa'atau created the space for the overlapping Stortoni to race through and touch down, Ruaridh Jackson adding the conversion.
Tiatia replied for the home side after a forceful break by Shane Williams and James Hook levelled the scores with a diagonal conversion.
Jackson's penalty edged Glasgow back into the lead but four kicks in quick succession by Hook provided a nine-point advantage for the Ospreys, who had been forced to replace Jonny Vaughton with Sonny Parker during the pre-match warm-up.
Max Evans split the Ospreys defence to set-up Fa'atau's first try in the corner but on this occasion Jackson was off target with the conversion attempt.
Hook then made a break for the line and though the Wales international was shackled by two Warriors defenders, Dan Biggar slipped a pass to Owen, who went over for the hosts' second try. Hook missed the conversion minutes before the break.
Jackson reduced Glasgow's deficit early in the second half before the visitors were dealt an injury blow.
Max Evans twisted his knee after landing awkwardly and was promptly stretchered off to be replaced by Tim Barker.
Hook was wide with his next penalty attempt but quickly made amends to restore the nine-point lead.
Warriors replacement Justin Va'a was sin-binned for killing the ball and from the resulting scrum, Nutbrown weaved his way through to touch down under the posts, giving Hook a simple conversion.
Persistent scrummaging infringements brought yellow cards for the home side's Paul James and Glasgow debutant Jon Welsh and the Ospreys' Marty Holah and Warriors' Moray Low were also sin-binned for tripping and foul play respectably.
Va'a and Fa'atau combined to allow the latter to notch his second try deep into added time and Jackson's missed conversion concluded play.
Ospreys coach Sean Holley: "We got on top just after half time and we looked to be playing some really good rugby.
"Unfortunately the game disintegrated with yellow cards. I don't think the officials got to grips with it.
"We got a good win at the end and hopefully the supporters have gone away happy."
Ospreys: Owen, A. Bishop, Hook, Parker, Williams, Biggar, Nutbrown, D. Jones, Hibbard, Griffiths, Gough, Wyn-Jones, R. Jones, Holah, Tiatia.
Replacements: Beck for Biggar (78), Shervington for Hibbard (66), James for Griffiths (66), Levi for Wyn-Jones (78), Tandy for Tiatia (73). Not Used: Wells, Bowe.
Glasgow: Stortoni, Faatau, M. Evans, Morrison, T. Evans, Jackson, McMillan, Welsh, Milligan, Low, Turner, Kellock, Palepoi, Forrester, Brown.
Replacements: Gregor for Stortoni (48), Henderson for M. Evans (48), O'Hare for T. Evans (73), Va'a for Welsh (56), McArthur for Milligan (48), Barker for Kellock (44), Eddie for Palepoi (41).
Ref: George Clancy