With this convincing bonus-point win, Glasgow Warriors moved themselves ahead of last night's opponents in the United Rugby Championship table and into the play-off places.
It was a particularly impressive performance and result because Danny Wilson’s side came into the match cold, with a Covid outbreak in the squad having caused their festive 1872 Cup double-header against Edinburgh to be postponed.
Perhaps unsurprisingly after three weeks of inactivity, Warriors did start slowly, and they fell behind to a second minute Gareth Anscombe penalty, conceded by Zander Fagerson for not rolling away from a tackle.
But the hosts kept their cool and worked their way deep into opposition territory before being awarded an offside penalty which Ross Thompson fired home to square it with just seven minutes played.
Frustratingly, Kiran McDonald failed to collect the restart, and when Zander Fagerson was penalised at the scrum, Anscombe fired Ospreys right back into the lead.
It was a game of cat-and-mouse at this stage, and now it was Warriors’ turn to win possession right back from the restart, giving Thompson a chance to square it when Jack Morgan went off his feet, but this time the young stand-off’s shot at goal was off target.
It proved to be a fairly inexpensive error because Warriors then claiming their first try when some powerful running in heavy traffic involving George Turner, Josh McKay and Sam Johnson creating a platform from which the ball was sent leftwards for Cole Forbes to finish off.
Thompson nailed the touchline conversion for good measure, but another penalty conceded soon after the restart let Anscombe pull it back to a one-point game.
Warriors picked up their second try when Sione Tuipoluto showed pace and power to brush off two tackles and run it home from halfway, with Thompson once again adding the extras.
A fourth Anscombe penalty – his 17th consecutive successful shot at goal this season – kept the visitors in touch, with scoreboard reading 17-12 at the break, although Rory Darge did have the visitors in trouble when he broke for the line just before the half-time whistle.
The home side fired out of the blocks at the start of the second period, pressurising Ospreys into conceding three penalties in quick succession, which allowed Thompson to kick to the corner.
But a mix-up between Johnson and Kyle Steyn in mdfield allowed Ospreys to snaffle possession and Luke Morgan cleared the danger.
Another rampaging run from Darge took Warriors right back into the strike zone, and they scored try number three a few phases later when McKay stepped back inside two Ospreys defenders and scooted over the line.
It looked like Warriors had claimed their bonus point try when Ali Price, McKay and Thompson combined to send Turner over, but referee Chris Busby correctly chalked it off for a forward pass.
However, it was only a matter of time before the home team struck again, and it was man-of-the-match Tuipulotu who did the damage, charging under the posts to set up an easy conversion for Thompson with just over an hour played.
Ospreys got a consolation try back with 10 minutes to go when Anscombe skipped through a gap and sent Dan Evans over.
But Warriors marched straight back up field and delivered the knock-out blow through a try for Fraser Brown, who was making his comeback after almost three months out with a knee injury.