The Ospreys and Glasgow were inseparable after 80-minutes of rugby after playing a match in awful conditions at the Liberty Stadium.
All 18 points came from the boots of fly-halves Gareth Owen and Dan Parks.
Owen was the two to one victor in the first half exchanges and the home fans sniffed victory when he added a third seven minutes after the break, but the Warriors fought back for Parks to level in the 65th minute with his third and final goal.
The result means Glasgow move into second place on the table with 19 points, tied with Ulster who they will face next week. The Ospreys remain in fifth place with 17 points.
It was a match where tactical kicking dominated at the expense of free-flowing rugby and scoring chances were few and far between.
Owen kicked penalties in the 12th and 25th minutes with Parks slotting one in between.
In the 33rd minute full-back Barry Davies’ burst almost led to hooker Richard Hibbard going over, but he was deemed to have fallen short of the line.
Glasgow often had the Ospreys‘ scrum in trouble as youthful props Cai Griffiths and Ryan Bevington found themselves under pressure.
However, the hosts managed to ride the Glasgow storm at that phase and five minutes after the break Owen extended his side’s lead.
Early in the second period the Ospreys also had veteran centre Sonny Parker to thank for the out-stretched arm that brought pacy Glasgow wing Thom Evans down.
Seven minutes after the break Owen stretched his side’s lead with his third penalty. Glasgow fought back to earn a brace of penalties which Parks had kicked by the 65th minute, bringing a justified reward for the visitors’ determination to match the hosts.
Owen led a break-out that brought another attempt at goal after Tiatia was held down after a tackle. But he failed with that 67th-minute shot and despite having the better chances as time wore on the visitors were unable to claim a vital winning score.
Owen narrowly failed with a long-range drop-goal attempt and after making a break down the touchline, wing Tommy Bowe could not find support.
