Nineteen of Medvedev's twenty-one championships have been earned on hard courts
A comeback the Russian player claimed his first title for over two years with a win over Frenchman Moutet in the Almaty Open final.
The athlete, a former top-ranked player, has endured a torrid period, winning just a single victory at the major tournaments and experiencing a meltdown at the American major.
The player's varied form on the ATP Tour - and struggles with his service game in particular - led to him dropping out of the top ten and eventually parting ways with long-term mentor Cervara.
Currently training with Johansson and Goetzke, Medvedev has consistently improved in the past month - culminating in a hard-fought competitive victory over challenger Moutet.
This represents his maiden championship since the 2023 Rome Masters and maiden on a hard surface since spring of that year.
Success also indicates the Russian has secured twenty-one titles at twenty-one various competitions.
"This marks the first occasion I'm at a tournament with my children at once, so to win a championship is especially meaningful," stated world number 14 the champion.
"This championship is in honour of my child my daughter, because the initial championship I got when my first daughter Alisa was delivered was for her."
The tennis star, the former major winner, had been defeated in his previous six title deciders, featuring in the German tournament earlier this year.
Medvedev's defensive play style and recurring outbursts on the playing surface had led observers to wonder if his skill to perform at the highest level was concluded.
But the athlete has altered his approach in the past month, striving to approach the net and perform aggressively, backed up by an better serving game.
Medvedev fought back from a deficit in the opening set against the tricky opponent, securing 4 of the final five exchanges to take the lead.
The competitors traded breaks in the second set before the Frenchman, bidding for his initial professional victory, seized the initiative to force a final set.
Moutet saved four early break points in a tight third set before the champion broke to fifteen to serve for the match.
Suitably, he clinched the title with a shot at the front of the court, with Moutet failing to manage a volley after a lengthy match.