Nineteen of the Russian's 21 victories have been earned on hard courts
A comeback Medvedev won his maiden championship for over two years with victory over Frenchman Moutet in the tournament final.
The Russian, a ex- number one, has endured a difficult season, winning just one win at the Grand Slams and suffering a setback at the US Open.
Medvedev's varied form on the ATP Tour - and issues with his serving in particular - resulted in him exiting of the elite rankings and finally separating with long-term mentor Gilles Cervara.
Currently training with Thomas Johansson and his other coach, the tennis star has steadily advanced in the recent weeks - climaxing in a closely contested competitive victory over Frenchman Moutet.
This represents his maiden championship after the Italian tournament and first on a hard court after that period of 2023.
The win also indicates he has achieved 21 championships at 21 distinct tournaments.
"For the first time I have attended a event with my two daughters together, so to win a title is especially meaningful," stated world number 14 Medvedev.
"This championship is in honour of my child her name, because the first title I achieved when my first daughter my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had lost his past six title deciders, comprising in that event previously this season.
His counter-punching approach and frequent outbursts on court had caused commentators to question if his capacity to perform at the top level was over.
Yet the player has altered his approach in recent weeks, striving to approach the net and perform aggressively, supported by an improved serve.
He fought back from a deficit in the opening set against the difficult opponent, winning four of the concluding five exchanges to gain the advantage.
Both players swapped breaks in the following set before the Frenchman, attempting for his maiden ATP Tour championship, gained dominance to force a final set.
He saved 4 early opportunities in a tight deciding set before the Russian secured a break to fifteen to serve for the match.
Suitably, Medvedev earned the title with a point at the front of the court, with his opponent unable to control a shot after over two and a half hours.
