Steve Tandy’s side suffered a shock 12-6 defeat in Italy on the opening weekend of last season but tries from hooker Scott Baldwin and wing Ben John ensured there was to be no repeat.
Treviso had won their five previous fixtures against Welsh regions at home and they made a strong start to the contest.
Outside half Alberto di Barnardo kicked an early penalty when Andrew Bishop was shown a yellow card for slowing the ball down.
Dan Biggar pulled the Ospreys level with a penalty before Treviso hooker Leonardo Ghiraldini was sent to the bin for collapsing the scrum and the visitors were rewarded for their decision to kick to the corner.
Hooker Baldwin peeled off the back of a driving lineout to go over in the corner and Biggar added a difficult conversion.
Two quick penalties from di Bernardo brought Treviso back to within a point before half time and they went in front shortly after the interval through another penalty.
Their lead only last three minutes when Biggar slotted a drop goal over from in front of the posts and young Ospreys wing John then went over in the corner for the Ospreys.
Biggar missed the conversation but made up for it with a second drop goal before a converted try from Treviso replacement Simone Favaro 15 minutes from the end set up a thrilling finish.
But a penalty from Biggar eight minutes from time settled the visitor’s nerves and Tandy’s side held on for the win.
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