19 of Medvedev's 21 titles have been earned on hardcourt
A comeback the Russian player claimed his maiden championship for over two years with victory over opponent Moutet in the Almaty Open final.
The athlete, a ex- number one, has endured a challenging year, managing just a single victory at the big events and experiencing a setback at the New York tournament.
Medvedev's varied form on the tennis tour - and struggles with his serving in particular - caused him exiting of the elite rankings and finally separating with long-term mentor his previous coach.
Currently working with Thomas Johansson and his other coach, he has gradually improved in the last few weeks - culminating in a closely contested three-set triumph over Frenchman Moutet.
This marks Medvedev's initial trophy since the Rome competition and first on a hard surface since that period of that year.
The win also indicates he has won 21 victories at 21 different events.
"For the first time I am participating in a event with my two daughters together, so to secure a trophy is particularly special," commented tennis professional Medvedev.
"This title is in honour of my younger daughter my daughter, because the first title I won when my older daughter her name was born was for her."
The tennis star, the past champion, had lost his past six championship matches, including in the German tournament in the past months.
Medvedev's counter-punching strategy and recurring emotional displays on the playing surface had prompted commentators to doubt if his ability to perform at the top level was over.
However the 29-year-old has made changes in the past month, attempting to advance forward and play positively, supported by an enhanced service.
Medvedev recovered from a disadvantage in the initial set against the difficult Moutet, taking four of the concluding five exchanges to go ahead.
The pair swapped service breaks in the second set before the Frenchman, bidding for his first ATP Tour title, took control to push for a third set.
Moutet rescued four initial chances in a competitive deciding set before the champion broke to fifteen to close out the victory.
Fittingly, the winner clinched the win with a rally at the front of the court, with the Frenchman unable to handle a shot after a lengthy match.
