Nineteen of the Russian's 21 championships have been achieved on hard surfaces
A resurgent the Russian player won his first championship for over two years with success over Frenchman Moutet in the Almaty Open title decider.
Medvedev, a former top-ranked player, has experienced a torrid period, winning just a single victory at the major tournaments and suffering a setback at the New York tournament.
His unpredictability on the ATP Tour - and difficulties with his serve in especial - led to him falling of the top ten and finally splitting with long-term coach his previous coach.
Now training with Johansson and his other coach, the tennis star has gradually progressed in the last few weeks - climaxing in a hard-fought 7-5 4-6 6-3 triumph over challenger Moutet.
This marks his maiden title after the Italian tournament and first on a hard surface from March of the previous year.
The win also signifies he has achieved 21 championships at 21 various competitions.
"For the first time I have attended a competition with my two daughters simultaneously, so to win a championship is especially meaningful," stated world number 14 Medvedev.
"This title is in dedication of my younger daughter her name, because the initial championship I won when my child Alisa was delivered was for her."
The tennis star, the past champion, had been defeated in his past six finals, featuring in that event earlier this year.
Medvedev's defensive approach and frequent outbursts on the playing surface had prompted commentators to wonder if his ability to play at the elite level was over.
Yet the 29-year-old has made changes in the last few weeks, making an effort to advance forward and compete assertively, backed up by an improved serve.
Medvedev recovered from a break down in the first set against the challenging Moutet, securing four of the concluding five exchanges to go ahead.
The pair traded break points in the middle set before Moutet, striving for his initial professional victory, gained dominance to push for a third set.
The opponent saved 4 early chances in a close third set before the champion won the break to that score to secure the win.
Suitably, Medvedev clinched the title with a rally at the front of the court, with his opponent incapable to manage a volley after two hours and 38 minutes.
