Nineteen of Medvedev's 21 victories have been earned on hardcourt
A comeback the Russian player secured his first trophy for nearly 30 months with success over opponent Moutet in the competition title decider.
The athlete, a ex- world number one, has endured a difficult season, winning just one match at the big events and experiencing a difficult moment at the US Open.
His varied form on the ATP Tour - and struggles with his serve in especial - resulted in him exiting of the elite rankings and eventually splitting with long-term mentor Gilles Cervara.
Currently collaborating with Johansson and his other coach, the tennis star has consistently advanced in the past month - culminating in a hard-fought competitive victory over Frenchman Moutet.
It is the player's maiden championship since the 2023 Rome Masters and initial on a hardcourt since March of 2023.
The win also indicates he has secured twenty-one championships at twenty-one various events.
"For the first time I'm at a competition with my children at once, so to secure a title is especially meaningful," said world number 14 Daniil Medvedev.
"This victory is in tribute of my second daughter my daughter, because the initial championship I achieved when my first daughter my daughter was born was for her."
Medvedev, the 2021 US Open champion, had lost his last six championship matches, comprising in that event earlier this year.
The player's retrieving strategy and recurring emotional displays on the tennis court had prompted commentators to question if his ability to perform at the top level was over.
Yet the athlete has implemented adjustments in recent weeks, striving to approach the net and compete aggressively, backed up by an enhanced service.
Medvedev recovered from a deficit in the initial set against the challenging opponent, taking four of the final five games to go ahead.
Both players swapped break points in the middle set before Moutet, attempting for his first professional championship, took control to force a final set.
The opponent rescued four early chances in a close deciding set before the champion won the break to 15 to serve for the match.
Fittingly, he clinched the title with a shot at the net, with Moutet unable to manage a volley after over two and a half hours.