Glasgow recorded their first ever win on Ospreys soil on Friday with 26-20 victory that could have serious implications in the race for the Pro12 play-offs.
Both sides harboured ambitions to secure a play-off place in this crucial but ill-disciplined match in Swansea.
The Ospreys early pressure almost led to a try for Hanno Dirksen but the in-form winger was brilliantly tackled on the line by a determined Chris Fusaro.
Ruaridh Jackson's penalty gave the Glasgow side the early lead.
The lead did not last long though as Dirksen eventually crossed for a try.
The Warriors were ahead again after their driving maul enabled Jon Welsh to score.
Ospreys captain Tom Smith was sin-binned for a cynical penalty at the ruckand Jackson's ensuing penalty extended their lead to 13-7.
Glasgow's Colin Shaw exposed sloppy Ospreys defence to score. Jackson added the extra's to give the visitors a 20-7 lead.
A Dan Biggar long-range penalty reduced the deficit to 20-10 on the stroke of half-time.
A scrappy start to the second half saw Biggar and Jackson exchange penalties. The Ospreys' chances of a comeback were dealt a severe blow when Ryan Bevington was sin-binned for tacking out the jumper in the line-out. Jackson added to his points tally to further put the Warriors ahead 26-13.
Referee Neil Paterson produced his third and fourth yellow cards of the game in quick succession. Firstly, Glasgow captain Al Kellock was penalised for an off-the-ball incident and Warriors replacement Johnnie Beattie for a dangerous tackle.
The two-man advantage enabled Ospreys replacement Kahn Fotuali'I to score.
Matthew Morgan's successful conversion may have earned the Ospreys a losing bonus point, but the result was just the second time the Ospreys had lost at the Liberty stadium in the tournament since 2010.
Tries: Dirksen, Fotuali'i
Cons: Biggar 2
Pens: Biggar 2
Tries: Welsh, Shaw
Pens: Jackson 4
Yellow cards: Bevington (Ospreys 65th min); Smith (Ospreys 25th min); Kellock (Glasgow - 68th min); Beattie (Glasgow - 74th min)
Ospreys: 15 Ross Jones, 14 Hanno Dirksen, 13 Andrew Bishop, 12 Ashley Beck, 11 Eli Walker, 10 Dan Biggar, 9 Rhys Webb, 8 Joe Bearman, 7 Sam Lewis, 6 Tom Smith (capt), 5 James King, 4 Ian Gough, 3 Joe Rees, 2 Richard Hibbard, 1 Ryan Bevington.
Replacements: 16 Scott Baldwin, 17 Will Taylor, 18 Aaron Jarvis, 19 Jonathan Thomas, 20 George Stowers, 21 Kahn Fotuali'i, 22 Matthew Morgan, 23 Tom Isaacs.
Glasgow: 15 Peter Murchie, 14 David Lemi, 13 Alex Dunbar, 12 Federico Aramburu, 11 Colin Shaw, 10 Ruaridh Jackson, 9 Henry Pyrgos, 8 Ryan Wilson, 7 Chris Fusaro, 6 Calum Forrester, 5 Al Kellock (capt), 4 Tom Ryder, 3 Jon Welsh, 2 Dougie Hall, 1 Ryan Grant.
Replacements: 16 Pat MacArthur, 17 Gordon Reid, 18 Ed Kalman, 19 Rob Verbakel, 20 Scott Wight, 21 Murray McConnell, 22 Johnnie Beattie, 23 Tommy Seymour.
Venue: Liberty Stadium
Referee: Neil Paterson (Scotland)