Treviso, yet to record a win this season, were in with a chance of breaking that duck as they held an 18-16 half-time lead thanks to tries from Luca Morisi and Benjamin Vermaak, with Tom Isaacs crossing for the Welsh outfit.
But Ospreys captain Justin Tipuric continued his recent good form with the only try of the second half, while Dan Biggar kicked 19 points in all to help their side to a third successive win.
Newport Gwent Dragons recorded their first RaboDirect Pro12 win of the season when they beat Aironi 23-14 at a rain-lashed Rodney Parade.
The Dragons crossed for two tries to one but were made to sweat on the win by the determined Italians, who were within a score of their hosts in the closing stages.
It is a defeat that leaves Aironi, who have 10 players on World Cup duty with Italy, still searching for their first away win since joining the Celtic League.
Peter Horne came off the bench to score a crucial second-half try as Glasgow Warriors recorded a 23-19 victory at Leinster.
Leinster's 28-match winning streak in regular-season games at the RDS was brought to an end in the RaboDirect Pro12 clash, despite the province enjoying the majority of possession and plenty of time in the visitors' 22.
The hosts' attack was well off its best in a below-par display with lock Nick Campbell, who touched down for a first-half try, and place-kickers Scott Wight and Duncan Weir completing the Scottish side's scoring.
Munster secured their first bonus-point victory of the RaboDirect PRO12 campaign as they broke clear of the Scarlets in the second half to win 35-12.
Doug Howlett scampered over for a try and the home pack also earned a penalty try as Munster took a 20-9 lead into the break.
Four penalties from Dan Newton and a monster effort from debutant Dale Ford kept the Scarlets in contention.
But the Munster bench had a considerable say in the closing stages, with replacements Duncan Williams and Tommy O'Donnell helping themselves to tries.
- Related links