Teenage fly-half Matthew Morgan saved the Ospreys' blushes with a 79th-minute penalty to level the scores at Treviso in the Heineken Cup.
Morgan, 19, made his tournament debut as a replacement 10 minutes earlier.
Hosts' prop Michele Rizzo, wing Benjamin da Jager and scrum-half Tobias Botes went over and fly-half Kristopher Burton kicked 11 points.
Tommy Bowe and Ryan Jones scored Ospreys tries, Dan Biggar kicked 13 points and Morgan added his penalty.
The Ospreys did enough to stay top of Pool Five as Biarritz beat Saracens, who earned a bonus point in defeat to leave the English and Welsh teams on six points with the French side a point behind.
Adam Jones cried off because of a calf injury to force a late Ospreys change.
Aaron Jarvis went in at tight-head with Cai Griffiths coming on to the bench.
The visitors were also without Alun Wyn Jones (dislocated toe) so Ryan Jones started in the second-row while Huw Bennett (neck) was also absent.
However, back-rowers Justin Tipuric and Jonathan Thomas joined wing Bowe in passing late fitness tests.
Lock Cornelius van Zyl made his 100th appearance for the hosts.
Fly-half Burton kicked the game's first points with a fourth-minute penalty as Treviso's pack made their mark in the opening exchanges.
Biggar failed with his first attempt at a response, then lock Jones attempted a 40-metre drop-goal in the knowledge the Ospreys had a penalty award to fall back on.
Jones' shot went wide, but Biggar then sent his penalty attempt in the same direction.
However, the Ospreys had signalled their threat with ball in hand on several occasions.
And when Richard Fussell burst down the left flank, space opened up further infield for Bowe to exploit.
The Irish star made the most of the opportunity, twisting and turning through a tackle before placing the ball backwards to score and Biggar converted.
Burton and Biggar exchanged penalties with the former putting his side within a point at the break with his third successful shot at goal.
But before the final whistle of the opening period, Ospreys scrum-half Kahn Fotuali'I departed nursing a rib injury to be replaced by Rhys Webb.
The hosts deservedly went back into the lead three minutes after the break, launching a line-out drive before prop Michele Rizzo charged over.
Burton converted and Biggar replied with a penalty to keep the contest finely balanced after the hosts illegally halted an Ospreys attack five metres from their line.
At the other end only Shane Williams stood between 6ft 4in wing de Jager and the line from a superb set-piece line-out move.
Williams had little chance after the Ospreys defence was opened up in front of him and de Jager crashed over.
Burton was unable to convert.
And when Ryan Jones seized his chance to go over after a line-out overthrow by hooker Enrico Ceccato to touch down, Biggar's conversion put the visitors back within a point of the hosts.
Having given the Ospreys a try, the hosts then took one back spectacularly.
Centre Tommaso Benvenuti drew Ashley Beck out of position before sending Botes on a 30-metre sprint to the line.
Burton's conversion attempt from wide on the left drifted wide and the hosts went down to 14 men when Benvenuti was sin-binned in the 61st minute, perhaps harshly, for a tip-tackle on wing Williams.
Biggar's penalty added to Benvenuti's sense of injustice, but even with the one-man advantage, the Ospreys were unable to break a resilient home defence.
The home side also held out against the Ospreys' increasingly desperate attacks from all parts of the field as the clock wore down.
But they were penalised in the 79th minute wide on the right and, with Biggar off the field, diminutive Morgan proved equal to the challenge of an angled, 50-metre shot.
Treviso: L Nitoglia; B de Jager, T Benvenuti, A Sgarbi, B Williams; K Burton, T Botes; M Rizzo, E Ceccato, L Cittadini, A Pavanello (capt), C van Zyl, B Vermaak , A Zanni, R Barbieri
Replacements: F Semenzato for Nitoglia (51), I Fernandez Rouyet for Rizzo (68), P Di Santo for Cittadini (53), M Vosawai for Vermaak (53), G Padro for Barbieri (70).
Not Used: Sbaraglini, Bernabo, de Waal.
Sin Bin: Benvenuti (61).
Ospreys: Richard Fussell; Tommy Bowe, Andrew Bishop, Ashley Beck, Shane Williams; Dan Biggar, Kahn Fotuali'i; Duncan Jones, Richard Hibbard, Aaron Jarvis, Ryan Jones, Ian Evans, George Stowers, Justin Tipuric (capt), Jonathan Thomas.
Replacements: Replacements: M Morgan for Fussell (69), T Isaacs for Biggar (70), R Webb for Fotuali'i (39), R Bevington for D Jones (44), C Griffiths for Jarvis (70), J Bearman for Evans (48), I Gough for Stowers (74).
Not Used: M Davies.
Ref: Pascal Gauzere (France).