19 of Medvedev's 21 victories have been achieved on hardcourt
A comeback the Russian player claimed his first trophy for 882 days with a win over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- world number one, has had a challenging season, managing just a single victory at the big events and suffering a difficult moment at the American major.
The player's inconsistency on the professional circuit - and issues with his serve in specific - resulted in him dropping out of the world's top 10 and eventually separating with long-term mentor his previous coach.
Presently training with Johansson and his other coach, the tennis star has consistently progressed in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 win over opponent Moutet.
This represents his first trophy after the Rome competition and initial on a hard court since spring of 2023.
Victory also means Medvedev has secured 21 titles at 21 distinct tournaments.
"For the first time I have attended a event with my both daughters together, so to get a championship is particularly special," commented tennis professional the champion.
"This victory is in honour of my younger daughter her name, because the maiden victory I got when my older daughter her name was delivered was for her."
The tennis star, the former major winner, had failed in his last six championship matches, including in the German tournament previously this season.
Medvedev's defensive approach and regular outbursts on the tennis court had caused some to wonder if his ability to compete at the highest level was over.
Yet the player has implemented adjustments in the last few weeks, striving to advance forward and perform aggressively, backed up by an better serving game.
The champion fought back from a break down in the first set against the tricky Frenchman, taking 4 of the concluding five points to go ahead.
The pair swapped break points in the second set before Moutet, attempting for his first professional title, gained dominance to push for a third set.
The opponent saved 4 early-game break points in a competitive third set before the Russian secured a break to fifteen to serve for the match.
Suitably, he clinched the title with a rally at the net area, with his opponent failing to manage a return after over two and a half hours.