The Ospreys left Scotstoun with a losing bonus point after a wet and windy 80 minutes on Friday night.
Sam Davies got the game underway, with the swirling Scotstoun wind behind him.
The first opportunity of the game went the way of the Ospreys, after they had won possession from a Glasgow put in to the scrum on halfway, the visitors eventually out to the left wing where Cory Allen attempted to dink it through for Luke Morgan to chase. The ball went loose, Sam Cross hacked it forward over the line, but Ruaridh Jackson got back to cover.
Glasgow enjoyed a spell of possession in and around the Ospreys 22, failing to get any real traction from their lineout drive on several occasions, before a great break from Cross saw the flanker carry from halfway to the Warriors 22 before feeding Tom Habberfield on his outside. The scrum half pinned his ears back and went for the line but he was pulled down by Nick Frisby just three metres short of the line.
Davies had a chance to give his team the lead in the 23rd minute after Glasgow were penalised for not rolling away but Davies pushed his kick across the face of the posts and wide.
Back came the home team and Luke Morgan had to be alert to snuff out the danger after Niko Matawalu put the ball behind an organised Ospreys defensive line for Kevin Bryce to chase.
Conditions were making it an error strewn game, both sides frequently losing possession through unforced mistakes, but it was the Ospreys who eventually broke the deadlock 32 minutes in, Davies making no mistake from the left after Glasgow interference at the lineout.
As the break approached a huge Ospreys scrum on the opposition 10m line was rewarded with a penalty, Davies went for the posts inside the final minute of the half but his kick never looked like hitting the target.
HALF-TIME: GLASGOW WARRIORS 0-3 OSPREYS
The hosts were level just three minutes after the restart, Brandon Thomson making no mistake after the Ospreys collapsed the maul.
As Glasgow enjoyed the better of the early exchanges, a scrum penalty allowed them to move into the Ospreys 22 where they went through phase after phase, inching their way ever closer to the line. It was eventually moved wide to Stafford McDowall, the centre hitting the line at pace. He was hauled down inches from the line by Rob McCusker, and Olly Cracknell was able to steal possession, allowing Habberfield to clear to touch.
Glasgow continued to dominate territory and possession, the Ospreys looking relatively comfortable absorbing their pressure, but they suffered a blow just before the hour when Gareth Thomas was stretchered from the field after lengthy treatment for a leg injury, replaced by Rowan Jenkins.
When play resumed it was Glasgow on the attack, a penalty against Scott Baldwin allowing Thomson to double his team’s tally for the night to put the home team 6-3 ahead after an hour.
The lead was six points just a couple of minutes later, Thomson using the wind to put one over from four metres inside his own half, straight down the middle.
With 10 minutes to go a moment of indiscipline from Matawalu on a rare Ospreys excursion into Glasgow territory saw the Fijian shown a yellow card for a deliberate knock on, meaning the Ospreys would play out the game with an extra man.
The Ospreys looked to set up camp in the Glasgow 22, searching for the winning score as the clock ticked towards 80 minutes. Luke Morgan jinked his way close to the line but just as it seemed the Ospreys would find a way through to pinch it they were penalised at the breakdown, allowing Glasgow to clear.