Their hosts, meanwhile, remain winless in five attempts but had Luca Redolfini's second-half try to show for their efforts.
Wales international Biggar, though, was at his imperious best with the boot for Steve Tandy's troops, who welcomed back Wales prop Adam Jones for his first RaboDirect PRO12 start of the season.
Biggar also added a second-half try to Richard Fussell and Jonathan Thomas efforts in the first half.
After missing his first attempt at the posts on three minutes, Biggar made amends by slotting away the opening points of the game with a sixth-minute penalty.
Gonzalo Garcia, taking over kicking duties for the Parma-based side who were without injured fly-halves Luciano Orquera and Paolo Buso, responded five minutes later with a kick of his own.
Biggar was not to be upstaged though and calmly added a further six points midway through the first half with two penalties as the Liberty Stadium outfit settled into their stride.
Fussell, who grabbed his first RaboDirect PRO12 try of the season against Munster last week, then made it two in two games when he crossed in the 28th minute.
Biggar slotted the conversion to take his personal tally to 11 points.
Then, just before the break, Ospreys all-but put the game to bed when flanker Thomas went over for his first of the campaign.
Biggar's missed conversion offered the Italians hope and Australian full-back Daniel Halangahu reduced Treviso's half-time deficit to 21-6 with a late penalty.
Buoyed by the points just before the interval, prop Redolfini crashed over on 43 minutes to the delight of the Stadio XXV Aprile faithful, who had only previously witnessed a 30-17 defeat to Connacht in early September.
Halangahu slotted away the conversion and the game was seemingly back in the balance.
Garcia missed his second penalty of the evening on 51 minutes but Halangahu showed him how to do it moments later to bring them within touching distance of the visitors.
But Biggar kept them at bay with another three-pointer and added further distance between the sides with his fifth penalty of the game.
His decisive blow though came with eight minutes remaining - the 22-year-old crossing and converting to secure a vital victory for the visitors.
|Zebre Score Card|
|Ospreys Score Card|