Pivac's troops were 17 points to the good at half-time, with Aled Davies and Hadleigh Parkes crossing over allied to Aled Thomas' seven points from the tee.
Dries van Schalkwyk's try-double made things dicey for the hosts but Steve Shingler's late penalty took even a losing bonus points tantalisingly out of reach for the Italians.
Scarlets have still lost just once in the GUINNESS PRO12 this season and are currently in second place, two points behind Connacht.
However, there are just six points separating the top five and Pivac belives a resurgent Ospreys - semi-finalists last year - will throw their name into the mix sooner rather than later.
"I think the Ospreys are going to have a good strong run home," said Pivac. "I think they have turned a corner and have some big hitters back on the park, players like Alun Wyn Jones had a big influence on their win over the Blues.
"They won't be panicking and they will be backing themselves to make that top six.
"That win over Zebre was critical for us because anything but a win would have been a disaster."
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