Nineteen of the Russian's 21 titles have been achieved on hard surfaces
A resurgent Medvedev won his maiden trophy for over two years with success over opponent Moutet in the Almaty Open title decider.
Medvedev, a ex- top-ranked player, has had a challenging season, winning just a single victory at the big events and suffering a setback at the US Open.
His varied form on the tennis tour - and difficulties with his serve in specific - resulted in him dropping out of the world's top 10 and eventually parting ways with long-time coach Gilles Cervara.
Presently working with his coach and Rohan Goetzke, the tennis star has consistently improved in the last few weeks - culminating in a closely contested competitive triumph over Frenchman Corentin Moutet.
It is his first trophy after the 2023 Rome Masters and first on a hardcourt after that period of that year.
Success also means the Russian has secured twenty-one victories at twenty-one different competitions.
"This marks the first occasion I have attended a competition with my children simultaneously, so to win a championship is especially meaningful," said tennis professional the champion.
"This championship is in dedication of my second daughter her name, because the initial championship I won when my child my daughter was born was for her."
The athlete, the 2021 US Open champion, had lost his previous six finals, comprising in that event in the past months.
Medvedev's defensive strategy and frequent emotional displays on court had caused observers to wonder if his ability to perform at the top level was concluded.
But the player has altered his approach in recent weeks, striving to advance forward and compete assertively, supported by an improved service.
Medvedev fought back from a break down in the initial set against the challenging opponent, taking four of the concluding five points to take the lead.
The pair swapped break points in the middle set before the Frenchman, striving for his maiden tour victory, took control to force a third set.
Moutet saved four early chances in a tight third set before Medvedev secured a break to 15 to close out the victory.
Appropriately, the winner clinched victory with a point at the front of the court, with Moutet failing to manage a volley after two hours and 38 minutes.
