Nicky Smith, Rhys Webb, Jeff Hassler, Scott Baldwin and Hanno Dirksen all crossed the Treviso line, with last season;s Wales Under 20 loose head prop Smith also carrying off the man of the match award.
Powerful No 8 Dan Baker had a hand in three of the tries while Dan Biggar kicked 17 points to complete a comfortable win at the Liberty Stadium. Biggar kicked Ospreys 6-3 ahead before the front-row set-up the game’s opening try.
Smith dominated his opposite number, who was twice penalised five metres from their own line, at scrum time. That allowed Baker to surge forward from the third set-piece, followed from close-range by prop Smith whose try was reward for his work in the scrum.
Biggar converted and traded penalties with Joe Carlisle for a 16-6 lead before Webb stepped through for a try on the stroke of half-time. Treviso were reduced to 14 men at the start of the second half when referee David Wilkinson lost patience with prop Rupert Harden following another collapsed scrum.
Ospreys took full advantage by securing the bonus point against the 14 men and Baker was the catalyst for both tries with powerful breaks. The first was followed by Hassler who still had to force his way past two defenders to score before Baldwin sniped in for the fourth try.
Treviso, weakened by a tumultuous summer behind the scenes, grabbed a consolation try through Marco Fuser.
Morgan Allen spilled the chance to hit back but Treviso forward Salesi Manu was binned late on and Josh Matavesi’s pass sent Hanno Dirkson speeding for the corner.
Sam Davies converted from close to the touchline to add the icing to an impressive first outing.