Blindside flanker Viktor Kolelishvili and substitute Vasil Lobzhanidze scored a try each in the space of 12 minutes to put the hosts ahead, with Merab Kvirikashvili converting the second to send Georgia into the interval 12-8 ahead.
Japan retook the lead five minutes after the restart when right-winger Lomano Lemeki got the first of his two tries with a lung-busting 90-metre sprint, but the hosts were soon back in front.
Georgia's forward pack had dominated Japan throughout, and number eight Beka Bitsadze powered over the line to put his team back in control, with Kvirikashvili converting again.
The Georgia fullback struck a penalty to stretch their lead to 22-13, but Japan dug deep in front of a partisan crowd at the Mikheil Meskhi Stadium.
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Lemeki gathered Harumichi Tatekawa's well-placed kick for his second try and Tamura converted to trim Georgia's lead to two points.
The Blossoms got their passing game going and Tamura released Kenki Fukuoka to put Japan three points ahead, before converting another penalty four minutes from time to seal their fourth win in five tests against Georgia.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
