You have to go back to January for the last time the Warriors won on the road in the United Rugby Championship and they never really looked like altering that record on Saturday.
They were distinctly second best as the Ospreys contained them, curbing their opponents’ attacking verve which came to the fore so impressively last weekend against Cardiff.
In truth, the Ospreys were a step up from their Welsh rivals and in scrum-half Rhys Webb and wing Keelan Giles they had the game’s two outstanding performers. The latter scored two tries, both impressive finishes in their own ways.
Both teams lost their No 8s in the opening stages. Ethan Roots was first to depart, on a stretcher, after only eight minutes following a head knock. Jack Dempsey followed him off with rib damage, replaced by Ryan Wilson after 12 minutes.
The game settled into a territorial battle and although Ospreys had the better of the first quarter they had nothing to show for it.
The Welsh side thought they had made the breakthrough in the 23rd minute through Giles but Webb knocked the ball on before the winger touched down.
Giles was not to be denied. Six minutes later he gathered a bouncing ball on the left wing and produced a brilliant diving finish in the corner despite the combined efforts of Sam Johnson and Tom Jordan.
The Warriors had struggled to get going but they finally cut loose five minutes before half-time only to have the score chalked off by the TMO. Cole Forbes made all the running, taking the ball from his own 22. The ball was played through the hands of Seb Cancelliere and Ali Price before Johnson finished off a sparkling move.
Unfortunately for the visitors, Scott Cumming was adjudged to have knocked on when he won the turnover which started the move.
Anscombe rubbed salt in the wounds by stretching the Ospreys’ lead with a penalty but Jordan replied with one of his own as Glasgow finally got points on the board just before the break.
The Ospreys lost stand-off Anscombe early in the second half but it didn’t affect them unduly and they extended their lead with a try from Keelan. Jordan lost possession and Webb capitalised with a probing kick downfield. The race was on and the electric Keelan won it, leaving the Glasgow defenders in his wake as he ran in his second score. Jack Walsh, on for Anscombe, converted then added a penalty to put Ospreys 20-3 ahead as the game entered its final quarter.
Glasgow continued to huff and puff, kicking to the corner and trying to utilise their rolling maul, but sub hooker George Turner was denied on three occasions while Ospreys were down 14 men following Dan Lydiate’s yellow card.
The visitors’ failure to capitalise was punished when Michael Collins’ kick and collect caught Glasgow out. The centre passed to Walsh who looped the ball out to George North to finish. Reuben Morgan Williams, the substitute scrum-half, then notched the bonus-point try, darting over from a scrum five.
The Warriors produced a late rally to score two tries from close range through Oli Kebble and Thomas Gordon - both converted by Domingo Miotti - but it was all too late to make a material difference.
Scorers: Ospreys: Tries: Giles 2, North, Morgan Williams. Cons: Anscombe, Walsh 2. Pens: Anscombe, Walsh.
Glasgow Warriors: Tries: Kebble, Gordon. Cons: Miotti 2. Pen: Jordan.
Ospreys: Max Nagy; George North, Owen Watkin, Michael Collins, Keelan Giles (Luke Morgan 73); Gareth Anscombe (Jack Walsh 47), Rhys Webb (Reuben Morgan Williams 68); Nicky Smith (Rhys Henry 72), Scott Baldwin (Dewi Lake 55), Tomas Francis (Tom Botha 60), Adam Beard (Rhys Davies 72), Alun Wyn Jones, Dan Lydiate, Jac Morgan, Ethan Roots (Will Griffiths 8).
Glasgow Warriors: Cole Forbes; Sebastian Cancelliere, Sione Tuipulotu, Sam Johnson, Rufus McLean; Tom Jordan (Domingo Miotti 66), Ali Price (Sean Kennedy); Jamie Bhatti (Oli Kebble 45), Fraser Brown (George Turner 45), Zander Fagerson (Simon Berghan 45), Scott Cummings, Richie Gray (JP du Preez 56), Gregor Brown (Sintu Manjezi 75), Thomas Gordon, Jack Dempsey (Ryan Wilson 12).
Referee: Jaco Peyper (SARU)