19 of Medvedev's twenty-one titles have been achieved on hard courts
A comeback Medvedev claimed his first trophy for nearly 30 months with success over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- world number one, has had a difficult season, managing just one match at the big events and undergoing a meltdown at the New York tournament.
Medvedev's varied form on the ATP Tour - and struggles with his serve in specific - led to him exiting of the elite rankings and finally parting ways with long-term mentor his previous coach.
Currently collaborating with his coach and his other coach, the tennis star has steadily advanced in the last few weeks - peaking in a closely contested competitive victory over Frenchman Corentin Moutet.
It is Medvedev's first championship after the Rome competition and first on a hardcourt from that period of the previous year.
Victory also indicates Medvedev has achieved 21 victories at twenty-one various competitions.
"For the first time I'm at a competition with my two daughters simultaneously, so to secure a championship is especially meaningful," said world number 14 the champion.
"This championship is in tribute of my second daughter my daughter, because the first title I got when my first daughter her name was delivered was for her."
Medvedev, the former major winner, had failed in his previous six championship matches, featuring in Halle in the past months.
The player's retrieving play style and frequent emotional displays on the playing surface had prompted commentators to doubt if his skill to perform at the elite level was concluded.
But the 29-year-old has altered his approach in recent weeks, striving to approach the net and perform assertively, reinforced by an improved serve.
He came back from a disadvantage in the initial set against the tricky Frenchman, taking 4 of the concluding five games to take the lead.
The competitors swapped service breaks in the second set before Moutet, striving for his initial ATP Tour championship, took control to force a third set.
Moutet saved four early chances in a close final set before the champion broke to 15 to close out the victory.
Fittingly, the winner clinched victory with a rally at the net, with Moutet unable to manage a return after a lengthy match.