Since winning in Rome in May 2023, Medvedev, ranked 14 in the world, has lost six finals, including the US Open the same year, and the Australian Open the following January.
This year, he lost in the second round in Melbourne before going out in the first round at Roland Garros, Wimbledon and Flushing Meadows.
After the US Open, Medvedev started working with new coaches Thomas Johansson and Rohan Goetzke and responded by reaching the semi-finals in Beijing and Shanghai.
The 21st victory of his career also boosts his hopes of reaching the year-ending ATP Finals, moving him up three spots to 12th, just 875 points behind Lorenzo Musetti, who is in the eighth and final place.
"It is great. I was not super happy with how I played in some moments of the match, but to win feels amazing," said Medvedev.
"In the most important points I played good."
The Russian will compete in the ATP 500 in Vienna next week in an attempt to continue his climb up the rankings.
After two evenly matched sets, Medvedev took the upper hand in the decider.
Close to breaking at 2-1, with Moutet saving four break points, the former world No.1 managed to break the Frenchman's serve at 4-3 before closing out the match on his serve.
"The last game was incredible, and I am happy to win the title," said Medvedev.
"It continues my funny story of 21 titles in 21 different cities."
Corentin, 26, is still waiting for his first career title after a third final defeat following Doha in 2020 and in Mallorca this year.