The opening exchanges suggested no, as the Ospreys moved 15-3 ahead by the midpoint of the first half. Tries from full-back Lee Byrne and winger Nikki Walker gave the defending champions an early platform, with number 10 Dan Biggar kicking a conversion and penalty.
Scrum half Tobie Botes got Treviso back in touch with three well-struck penalties, but the Ospreys had the bonus point sewn up within eight minutes of the restart.
Centre Andrew Bishop and number 8 Jonathan Thomas touched down in quick succession to leave Treviso 27-9 adrift.
Welsh wing wizard Shane Williams crowned his first start of the season with a try, before the Italians gained some consolation with a late converted score from full-back Brendan Williams.
Williams was one of five changes Treviso coach Franco Smith made to the side that accounted for the Scarlets. His inclusion at full-back saw Italian international Luke McLean shift to the left wing. Up front, hooker Diego Vidal, lock Enrico Pavanello and number 8 Paul Derbyshire all came in for their first league starts.
The Ospreys management made two changes in personnel from last weekend's 27-26 loss to Ulster, drafting Byrne and Williams into the side at the expense of Sonny Parker and newcomer Richard Fussell.
In rain-soaked conditions in Swansea, both sides took time to adapt to the greasy ball. A fifth minute break by scrum half Jamie Nutbrown enlivened the 6,724-strong crowd, and a neat feed to the supporting Byrne produced the opening try.
Biggar converted but Botes replied for the visitors soon after, drilling a penalty over after Ospreys lock ian Evan was whistled up for not rolling away.
Gareth Owen, who operated at inside centre, lost control of the ball as he lunged for the try-line in a near miss for the Welshmen, who were beginning to boss proceedings.
But try number two duly arrived, in the 13th minute, through big Scottish winger Walker. A fluid back-line move, involving Biggar, Bishop and Byrne, saw the ball worked out to the right where Walker used his pace and power to cross for an unconverted try.
Biggar and Botes then traded penalties, with the latter's meaty effort from halfway just clearing the crossbar. The Treviso number 9 missed a subsequent kick as his forwards began to see more ball.
The Italian pack got close to the home try-line courtesy of some patient build-up, picking and driving through a number of phases. But their hard work was spoiled by a turnover and Biggar cleared the danger.
Treviso did get some reward for their improved play as an obstruction call against Ospreys hooker Mefin Davies allowed Botes boot Treviso to within six points at the break - 15-9.
However, that was as close as Smith's charges got. Biggar changed the point of attack in a flowing move and Bishop popped up on his shoulder to dart through a gap and score, as the Ospreys made a business-like start to the second half.
Biggar converted and, in the 49th minute, the hosts' fourth try was finished off by man-of-the-match Thomas, who emerged from a pile of bodies after a powerful close range shunt from the forwards.
Treviso threatened to hit back but a penalty miss from Botes and the sin-binning of winning Tommaso Benvenuti for killing the ball dented their hopes.
A chip ahead from replacement Tommy Bowe almost resulted in a second try for Byrne - television match offical Hugh Watkins ruled that the full-back had knocked on in his attempt to score.
With ball-handling particularly difficult in the heavy rain, there was little flow to the remaining minutes. The Ospreys used their numerical advantage to work an overlap for Williams to score, the winger doing really well to collect a low pass and score in the corner.
The Ospreys had to see out the game down to 14 men, with flanker and captain for the night Jerry Collins seeing yellow for a ruck offence. It was left to Treviso to again show their ability to score late - their match winner against the Scarlets arrived four minutes from time.
Williams managed to dot down under the posts, with TMO Watkins' backing. Fly-half Chris Burton added the extras for a Treviso outfit that battled right to the final whistle.
The result ended the Italians' nine-match unbeaten run in all competitions, which stretched back to April, and crowned a good day for the Ospreys who earlier had their four point Magners League deduction for this season overturned after an independent Celtic Rugby disciplinary appeal.
|Ospreys Score Card|
|Benetton Treviso Score Card|