Warriors made a great start with two tries in the opening minutes but Zebre were in control for the bulk of the first half and were unfortunate to trail at the break.
"We took a bit of stick at half time for compounding errors that let them back into the game," said man-of-the-match George Horne, who scored two of his team's eight touchdowns. "It wasn't easy kicking into that wind and we played up our own backsides a bit, but we got a bit of a speaking to at half time and did better in the second half.
"That was a massive win for us as we had let ourselves get a bit behind the top three in our Conference table and we know every game is a must-win one now."
Horne was denied a hat-trick only by a high tackle that won a penalty try and his display could put him in the reckoning for a starting spot in Scotland's team to face Italy next weekend.