Tries from Scott Baldwin and Ben John plus 14 points from the boot of Dan Biggar sealed an important victory for the Ospreys, who were made to work hard for their victory by a determined Treviso outfit.
The hosts led 12-10 at the start of the second half following four penalties from Alberto di Bernardo, while they then reduced the deficit to two points heading into the final quarter of an hour through Simone Favaro's try but Biggar's penalty effectively settled matters.
The visitors disappointingly missed out on the play-offs last season after a fifth placed finish, while Treviso settled for seventh.
It was the home side who went closest to breaking the deadlock early on as Di Bernardo missed with a drop-goal attempt, but the Argentinian-born Italy international made no mistake with a penalty after Ospreys centre Andrew Bishop was sin-binned for putting his hands in the ruck.
Treviso failed to make their man advantage count and Biggar levelled proceedings and in the process became the second leading all-time scorer in the competition.
Some faults in the maul saw referee Neil Paterson reach for a yellow card for a second time shortly after Bishop came back onto the field, this time Treviso were penalised as Leonardo Ghiraldini went to the bin.
The Welsh side, unlike their opponents, did capitalise on their advantage as they opted against a penalty and drove forward for the line, which was rewarded when hooker Baldwin crossed for the first try in the 23rd minute, with Biggar adding the conversion.
Di Bernardo scored two penalties just before the interval to reduce the deficit to one point at half-time and the 32-year-old added another three points to give Treviso the lead early in the second half.
A drop goal from Biggar re-established Ospreys' lead and the visitors went further in front when Tito Tebaldi's box kick brought an error from Treviso winger Luke McLean which allowed John to touch down in the right corner in the 59th minute.
Biggar missed with his conversion attempt but added another drop goal to give the Welsh region a 21-12 lead with 17 minutes remaining.
Treviso refused to give in, however, and Favaro barged over from a rolling maul, with Di Bernado adding the extras in the 68th minute to set up a frantic finale.
Biggar, however, gave Ospreys something of a cushion after slotting home a 74th-minute penalty and the visitors held on to walk away with the points.