The home side showed plenty of enterprise but not much accuracy, and things went from frustrating to embarrassing when the Warriors soaked up all the pressure and scored the opening try through scrum-half Sam Pinder. The Australian charged down a Shaun Connor clearance to score and Parks' extras gave the underdogs a healthy 10-0 lead, despite managing only two excursions into the Ospreys territory.
Mustoe tried his luck in the opposite corner in the 17th minute and opened the Welsh region's account with a well-taken try, but there was just enough time for Parks to bang over a penalty goal and the home side were booed off as they trailed 13-5 at the break.
Glasgow had the better of the opening tussles of the second half, courtesy of more Ospreys errors, but a break-out by Evans and Connor gave flanker Steve Tandy the space to dot down in the corner and it was game on. Connor levelled the scores with a penalty goal from in front in the 64th minute, and the tide began to turn in the Ospreys favour as the rain started bucketing down.
Parks tried to win it with a dropped goal, but it was never on target, and it was left to Henson to rescue things from 46 metres out.
Tries - R Mustoe, S Tandy
Pens - S Connor, G Henson
Try - S Pinder
Pens - D Parks 2
Con - D Parks
Halftime: Glasgow 13-5
Referee: Alain Rolland (Ireland)