The 6-7 (6-8) 6-1 6-3 win was a boost for the Russian'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," 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 the Georgian qualifier Basilashvili, ranked 128th in the world, clinched the set with a powerful cross-court backhand.
The world No.5 regained control in the second set, forcing backhand rallies and pressuring an error-prone Basilashvili into firing wide.
Basilashvili, playing in his first final on the tour since 2022, seemed to struggle 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.
Two other ATP finals staged in Europe on Sunday ended up with Medvedev being joined as a champion by Dutchman Tallon Griekspoor and Italian Lorenzo Musetti.
Griekspoor battled from a set down for a third consecutive match to beat Jan-Lennard Struff and win the European Open in Brussels 4-6 6-3 6-4, his first trophy this season.
In Lyon, Musetti was a 6-3 6-4 victor in the final against Taylor Fritz, who is also making a late push to make the ATP Finals.
The Italian star won his first tour-level title since 2022, after also having saved four match points against his compatriot Flavio Cobolli en route to victory in the semi-finals.
