Italy have scored four attempts, including one from Tommaso Allan, who also kicked two penalties and one conversion in the first meeting of the teams since 2003.
The game was seen as an unofficial test of Italy's right to remain in the Six Nations, where it has not won a match since 2015 and finished last in the last three seasons.
Georgia won the European International Championship – effectively a second-level event – for eight of the last 10 seasons, but there is no promotion and relegation between the two competitions.
After Allan converted a penalty kick early on, a stunning solo attempt by Georgia's Tamaz Mchedlidze and a conversion from Soso Matiashvili gave the visitors an early lead of 7-3.
But attempts by Michele Campagnaro and Mattia Bellini, with an allan penalty in the interval, gave Italy an advantage of 18 to 7 at halftime.
Italy increased their lead with more attempts from Simone Ferrari and Allan. Matiashvili converted a penalty and Georgia reduced the delay with a penalty attempt. (Written by Brian Homewood; Ken Ferris Edition)