The Warriors stayed on course for a Heineken Cup place next season with another impressive away win.
Three first half tries put the visitors’ well in command and Wales lock Brent Cockbain was able to plough over for the try that clinched the bonus point early in the second half.
With the battle for the four Welsh places in Europe’s top tournament next season being decided by Celtic League positions, the Warriors knew they would have to stay on terms with the Ospreys on the night to stay in the frame.
With Llanelli Scarlets leading the way in second place with 63 points, and The Dragons not far behind with 56 ahead of their clash on Saturday night with Cardiff Blues, it was vital the Warriors picked up points in Scotland.
Their bonus point victory means they are now in fourth place with 53 points, while the Ospreys’ thumping home win over The Borders took them up to 53 points in fifth. Cardiff Blues have 42 points with a game in hand.
The first of four penalties from new Scottish international stand-off Dan Parks gave Glasgow some early hope, but by the break Welsh scrum half Gareth Cooper had made one try and scored another as the Warriors got into their stride.
It was No 8 Richard Bryan who grabbed the first try for the Welshmen, rounding off a brilliant break by Wales centre Sonny Parker, and then Cooper darted away for his try. Then the Welsh No 9 chipped ahead to allow Parker to grab a third try before the break.
Ceri Sweeney’s boot ensured the Warriors were 22-12 ahead at the break.
Cockbain’s try secured the bonus point and Lions wing Dafydd James grabbed a fifth before Rory Kerr crossed for a consolation try for the home side.
There was still time for Gareth Wyatt to make it a round half-dozen tries for the Warriors and Neil Jenkins chipped in as a second half replacement for Sweeney with two conversions and a penalty to take his season’s tally to 256 points to lead the scoring tables by two from the Ospreys’ Gavin Henson.