Peter Horne emerged as the Warriors' hero, his 75th-minute penalty settling an enthralling contest that could well have been heading for a draw.
Glasgow were in the driving seat for much of the first half through Pat MacArthur's converted try but back came Ospreys, aided by 11 points from the boot of Sam Davies, and a Tom Grabham score.
Then two successive Horne penalties took the score to 19-16 and there it remained, with the Warriors now perched four points ahead of second-place Ulster in the GUINNESS PRO12.
Ulster themselves hung on by their fingernails to beat Edinburgh 20-17 at BT Murrayfield, despite having to cope with respective red and yellow cards for Stuart McCloskey and Franco van Der Merwe in the closing stages.
Edinburgh were looking on course for their ninth successive home win at half time - leading 14-10 through Phil Burleigh's try and fine kicking from Tom Heathcote - but the inspirational Ruan Pienaar kept Ulster close.
And Pienaar's points haul, allied to a Darren Cave try midway through the half, proved enough of a cushion before the final whistle blew.
Scarlets' duel with Munster was undoubtedly one of the clashes of the round, as Ian Keatley converted replacement JJ Hanrahan's last-gasp try to clinch a 25-25 draw for the visitors.
The Welsh region looked home and hosed after Hadleigh Parkes raced away for a second-half score, and with Steve Shingler heading for a 20-point haul with his boot.
But after Felix Jones scored a late try to add to youngster Jack O'Donoghue's earlier effort, the stage was set for Hanrahan as Scarlets finally crumbled under the weight of a George Earle yellow card.
The Ospreys, who led the GUINNESS PRO12 for so long, now find themselves in fifth after Leinster moved up into the top four with a 29-8 triumph over Zebre.
But it was far from routine, the Italians entering the break 8-3 to the good, before Jimmy Gopperth pulled off a rescue act with a 14-point haul and Sean Cronin grabbed a bonus-point try at the death.
Connacht remain in sixth and were helped along their way by a Rynard Landman red card, as they battled to a 30-25 win at Newport Gwent Dragons.
Landman was dismissed in the first half and though Dragons deserve full credit for fighting back - including a Hallam Amos double - scores from Mick Kearney, Eoghan Masterson and Craig Ronaldson meant Connacht were always out of reach.
And last but not least, full-back Jayden Hayward enjoyed an evening to remember, bagging 20 points as Benetton Treviso roared to their third GUINNESS PRO12 win of the season at the expense of Cardiff Blues.
TRY OF THE WEEKEND
Leinster's line may have been in disarray but the manner in which Zebre took advantage - at the RDS of all places - was explosive.
After fielding a kick, the Italians spread the ball out to the left and there was very little cover as Hennie Daniller stormed into open space.
He fed Andrea de Marchi - the prop having shown a surprising turn of pace to keep up with the No.15 - and he looped an exquisite pass over his shoulder to Michele Visentin while fending off two men.
Visentin then popped the ball to Daniller who finished what he started.
BREAK OF THE WEEKEND
This was not a break that left defenders trailing in its wake but Nick Williams showed that sheer physicality is a fine substitute for pace.
The Ulster No.8 barged through the gain-line, shrugging off WP Nel and then Tom Heathcote, before he offloaded at just the right time to send Darren Cave through for what proved to be the crucial try.
PLAY OF THE WEEKEND
Munster are nothing if not resilient and though replacement JJ Hanrahan stole the headlines with his last-gasp, match-tying try, the Irish province put on a lesson in patient teamwork as the clock turned red.
Felix Jones had clawed Munster back to within seven points just a few minutes before and a forwards drive inched them ever closer to the try-line.
Scarlets swarmed towards the breakdown and finally the ball came back inwards for Hanrahan to scoot across.
PLAYER OF THE WEEKEND
Benetton Treviso's display against Cardiff Blues was equal parts poise and power and no one epitomised this better than full-back Jayden Hayward.
The Kiwi's sidestep and break from halfway was one of a series of flashy tries, and he backed that up with 15 points from the tee on a fantastic night for the Italians.
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