Ali Price and Tim Visser crossed as the Scots built up a 15-3 half-time lead.
Ross Ford went over twice early in the second period before Damien Hoyland dived in for his first Scotland try, emulating Price's feat.
Michele Campagnaro and Angelo Esposito claimed second-half tries for Italy, who also had Dean Budd and Abraham Steyn sin-binned.
After the game, Gregor said: "To make the breakthrough at half-time gave us a big boost. We scored a couple of really good tries in the second half.
"As a coach, if you get a win and there's a few things to work on, you're very pleased.
"We knew it was going to be tough in the conditions, first time this team had played together but I was really pleased with the effort the guys put in throughout the game, especially defensively around the maul area, around the set piece, which is a bring strength of Italy's. We did that very well.
"It wasn't perfect. Sometimes how we wanted to attack, we saw that being transferred, other times we weren't there yet but I felt the guys kept working at it."