Nineteen of Medvedev's 21 titles have been won on hardcourt
A resurgent Medvedev claimed his maiden championship for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The athlete, a ex- world number one, has had a difficult year, managing just a single victory at the big events and experiencing a meltdown at the US Open.
The player's varied form on the ATP Tour - and difficulties with his serve in specific - led to him falling of the elite rankings and ultimately separating with former mentor Gilles Cervara.
Currently collaborating with Thomas Johansson and Goetzke, he has gradually improved in the recent weeks - climaxing in a hard-fought three-set win over opponent Moutet.
This marks his first title since the 2023 Rome Masters and initial on a hardcourt from March of 2023.
The win also signifies the Russian has achieved 21 victories at twenty-one different events.
"This marks the first occasion I am participating in a event with my two daughters together, so to secure a title is particularly special," stated world number 14 Medvedev.
"This victory is in honour of my child my daughter, because the initial championship I got when my older daughter Alisa was delivered was for her."
Medvedev, the past champion, had been defeated in his past six championship matches, including in the German tournament previously this season.
His retrieving strategy and recurring emotional displays on the tennis court had caused commentators to doubt if his capacity to perform at the elite level was over.
But the athlete has implemented adjustments in the last few weeks, making an effort to advance forward and play aggressively, backed up by an improved serving game.
The champion fought back from a deficit in the first set against the difficult opponent, securing four of the last five points to take the lead.
The competitors swapped service breaks in the following set before the challenger, striving for his initial tour victory, took control to create a third set.
The opponent rescued 4 early-game chances in a tight deciding set before Medvedev won the break to 15 to serve for the match.
Appropriately, the winner clinched the title with a rally at the front of the court, with Moutet incapable to manage a volley after over two and a half hours.