Italy scored four tries, including one by Tommaso Allan who also kicked two penalties and a conversion, in the first meeting of the sides since 2003.
The game was seen as an unofficial test of Italy's right to stay in the Six Nations, where they have not won a match since 2015 and have finished bottom for the last three seasons.
Georgia have won the Europe International Championships -- effectively a second-tier event -- for eight of the last 10 seasons but there is no promotion and relegation between the two competitions.
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After Allan converted an early penalty, a stunning solo try from Georgia's Tamaz Mchedlidze and a Soso Matiashvili conversion gave the visitors an early 7-3 lead.
But tries by Michele Campagnaro and Mattia Bellini, with an Allan penalty in between, gave Italy an 18-7 halftime advantage.
Italy increased their lead with further tries by Simone Ferrari and Allan. Matiashvili converted a penalty in between and Georgia reduced the arrears with a penalty try. (Writing by Brian Homewood; Editing by Ken Ferris)
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