19 of the Russian's twenty-one championships have been achieved on hard courts
A revitalized Medvedev claimed his initial trophy for nearly 30 months with victory over Frenchman Moutet in the Almaty Open championship match.
The athlete, a former world number one, has had a challenging year, managing just one match at the major tournaments and undergoing a meltdown at the US Open.
The player's varied form on the ATP Tour - and issues with his serve in especial - caused him exiting of the elite rankings and finally separating with long-term mentor Gilles Cervara.
Presently working with Thomas Johansson and Goetzke, he has gradually improved in the last few weeks - culminating in a hard-fought 7-5 4-6 6-3 win over challenger Moutet.
It is Medvedev's initial trophy since the Rome competition and initial on a hard surface since that period of the previous year.
Success also means the Russian has secured twenty-one victories at 21 various competitions.
"For the first time I'm at a tournament with my children at once, so to get a title is particularly special," stated ranked player the champion.
"This victory is in honour of my second daughter Victoria, because the initial championship I got when my child my daughter was delivered was for her."
The athlete, the former major winner, had failed in his last six championship matches, featuring in that event in the past months.
His retrieving play style and recurring emotional displays on the playing surface had prompted some to question if his skill to play at the highest level was finished.
Yet the athlete has altered his approach in the last few weeks, making an effort to advance forward and play assertively, supported by an enhanced serving game.
The champion came back from a deficit in the opening set against the tricky opponent, securing 4 of the final five exchanges to gain the advantage.
The competitors traded break points in the second set before the Frenchman, striving for his first professional championship, took control to push for a third set.
Moutet saved 4 initial opportunities in a tight final set before Medvedev won the break to fifteen to serve for the match.
Suitably, Medvedev earned the win with a rally at the net, with Moutet failing to control a volley after a lengthy match.