Nineteen of the Russian's 21 titles have been achieved on hard surfaces
A comeback Medvedev won his initial championship for over two years with success over opponent Moutet in the competition final.
The athlete, a ex- world number one, has experienced a difficult year, achieving just one win at the Grand Slams and suffering a setback at the US Open.
Medvedev's varied form on the ATP Tour - and struggles with his service game in specific - caused him falling of the world's top 10 and eventually splitting with long-time mentor his previous coach.
Presently working with Thomas Johansson and Goetzke, he has gradually improved in the past month - peaking in a hard-fought three-set victory over challenger Moutet.
This represents Medvedev's first championship following the 2023 Rome Masters and first on a hard surface from that period of the previous year.
Success also means Medvedev has secured 21 titles at twenty-one various tournaments.
"It's the first time I have attended a competition with my two daughters together, so to win a title is especially meaningful," said world number 14 the champion.
"This championship is in tribute of my child Victoria, because the maiden victory I got when my first daughter Alisa was born was for her."
The athlete, the former major winner, had lost his past six finals, including in that event earlier this year.
The player's retrieving play style and frequent emotional displays on court had caused commentators to wonder if his ability to perform at the highest level was concluded.
However the athlete has altered his approach in the last few weeks, attempting to approach the net and compete positively, supported by an improved serving game.
The champion recovered from a break down in the opening set against the tricky opponent, securing four of the last five exchanges to take the lead.
The competitors traded service breaks in the middle set before the challenger, bidding for his maiden professional championship, seized the initiative to create a final set.
He rescued 4 early opportunities in a close deciding set before the Russian secured a break to that score to secure the win.
Appropriately, Medvedev earned victory with a point at the net, with Moutet unable to manage a return after over two and a half hours.
