After the break, Tom Smith went over for the visitors, after Tom Isaac's first-half score, but the Ospreys were living dangerously until Kristian Phillips kicked a pressure penalty late on with Biggar in the sin bin.
And while Holley believes there is plenty of room for improvement, he's convinced Treviso will cause a few upsets on home soil in this season RaboDirect Pro12.
"It was a hard earned win, we really had to fight for everything," said Holley. "We didn't play great, but we dug in well and showed a lot of resolve at the end to make sure of the win.
"Treviso will claim a lot of scalps here this season, just as they did last year. They are a very difficult team to play against and some good sides have come away from here beaten.
"Teams don't relish coming here, that's for certain, so although we aren't happy about how we played we are pleased with the win.
"Treviso made life very difficult for us. When we were able to get to grips with them, particularly in the second half, keep the ball and go through phases, then we looked more threatening, but it wasn't a great performance by any stretch of the imagination.
"We saw some excellent goal-kicking from Dan Biggar, he punished them from all areas of the field, but then when we lost him for the closing stages we showed a lot of resolve and determination to stick in there for the win.
"We used the bench well and had a younger group of players on by then, who saw us through in the end."
But while Holley singled Biggar out for praise, he also identified his side's current weaknesses, suggesting his side must keep their feet on the ground despite their unbeaten start to the season.
"We've got three wins from three and that's a good start considering we aren't playing as well as we can do," he added.
"There's been plenty to be happy about, endeavour, effort and plenty of resolve, but we can still play a lot better.
"There's still a lot of work to do, particularly in the lineout and tackle area, so we aren't getting carried away and won't allow anyone within the group to get carried away."
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