The win was a boost for Medvedev's hopes of securing his place early in the ATP Finals, which he won in 2020.
Alexander Zverev, Carlos Alcaraz and Ben Shelton have already qualified for the tournament, while the injured Jannik Sinner will not feature in the eight-man season finale in Turin from November 15-22.
"I always said, it's just a matter of luck, time, moment," said Medvedev after the first successful title defence of his career.
"I was feeling fresh, I was feeling physically good... I'm happy to finally do it I guess," the 30-year-old added with a smile.
Former US Open champion Medvedev saved two set points to force a tiebreak in the first set, but netted two attempted winners as qualifier Basilashvili, ranked 128th in the world, clinched the set with a powerful cross-court backhand.
The world number five regained control in the second set, forcing backhand rallies and pressuring an error-prone Basilashvili into shooting wide.
Georgian Basilashvili, playing in his first final on the tour since 2022, struggled with his nerves in the third set, netting a backhand drop shot to bring up Medvedev's first match point, before shooting wide from the baseline to lose the match.
Medvedev is set to play in the Vienna Open starting on Monday, and the Paris Masters from October 31, as he looks to secure his place in Turin.
Click here for more on the match
