19 of the Russian's 21 titles have been won on hard courts
A revitalized Medvedev secured his maiden trophy for 882 days with success over opponent Moutet in the Almaty Open title decider.
The Russian, a ex- world number one, has endured a torrid season, managing just one match at the big events and suffering a meltdown at the American major.
The player's varied form on the tennis tour - and struggles with his serving in specific - caused him exiting of the elite rankings and finally separating with long-term coach his previous coach.
Presently collaborating with Johansson and Goetzke, the tennis star has steadily improved in the last few weeks - peaking in a hard-fought three-set triumph over Frenchman Moutet.
This marks Medvedev's maiden title after the 2023 Rome Masters and maiden on a hard surface from spring of 2023.
Victory also means the Russian has won 21 titles at 21 various events.
"For the first time I am participating in a event with my both daughters at once, so to win a trophy is particularly special," stated world number 14 Daniil Medvedev.
"This victory is in tribute of my child my daughter, because the first title I won when my first daughter her name was delivered was for her."
The athlete, the former major winner, had lost his last six championship matches, featuring in Halle in the past months.
The player's defensive approach and recurring reactions on court had caused commentators to question if his skill to play at the top level was finished.
Yet the athlete has implemented adjustments in recent weeks, attempting to come to the net and perform positively, backed up by an improved service.
He fought back from a break down in the first set against the difficult Frenchman, taking 4 of the concluding five points to gain the advantage.
The pair swapped break points in the following set before Moutet, bidding for his first ATP Tour title, gained dominance to force a decider.
The opponent rescued 4 early chances in a close third set before the champion secured a break to 15 to close out the victory.
Appropriately, Medvedev clinched the title with a point at the net, with his opponent incapable to handle a volley after over two and a half hours.