The Welsh side had to battle back from 18 v 16 down at the break but controlled the second period and captain Justin Tipuric try just after the interval was the difference between the sides.
Treviso were still hunting their first victory of the season but started well in Northern Italy.Â
Kris Burton and Biggar exchanged early penalties before Luca Morisi and Benhamin Vermaak crossed for tries for the host. Tom Isaacs grabbed a converted try just before the break for the 2010 PRO12 Champions to leave them just two points adrift.
Tipuric scored his try just two minutes into the second period and Biggar then kept his side in front with 6 points with the boot as the Ospreys controlled proceedings.
Willem de Waal kicked three second-half penalties for Treviso to kept them in touch but it wasn’t enough and the Ospreys march on unbeaten.
