Nineteen of Medvedev's twenty-one championships have been achieved on hardcourt
A comeback Medvedev claimed his maiden championship for 882 days with success over Frenchman Moutet in the Almaty Open title decider.
The athlete, a former number one, has had a difficult season, achieving just one win at the big events and suffering a setback at the American major.
Medvedev's inconsistency on the tennis tour - and struggles with his service game in specific - led to him falling of the top ten and eventually parting ways with former coach Cervara.
Now working with Johansson and his other coach, the tennis star has consistently progressed in the last few weeks - peaking in a hard-fought three-set win over opponent Moutet.
This marks Medvedev's maiden trophy since the Rome competition and initial on a hardcourt since that period of the previous year.
Success also indicates he has secured 21 championships at 21 different tournaments.
"For the first time I am participating in a competition with my children at once, so to secure a trophy is particularly special," commented world number 14 the champion.
"This victory is in honour of my younger daughter her name, because the first title I won when my first daughter Alisa was delivered was for her."
Medvedev, the past champion, had failed in his last six championship matches, featuring in the German tournament earlier this year.
Medvedev's retrieving strategy and recurring emotional displays on the playing surface had prompted commentators to question if his skill to play at the elite level was over.
Yet the player has implemented adjustments in the last few weeks, striving to approach the net and perform aggressively, reinforced by an better service.
He recovered from a deficit in the opening set against the difficult Moutet, taking four of the last five points to take the lead.
The pair exchanged service breaks in the following set before the Frenchman, striving for his maiden tour victory, gained dominance to push for a final set.
The opponent defended four early break points in a tight third set before the Russian won the break to fifteen to close out the victory.
Fittingly, Medvedev secured victory with a shot at the front of the court, with Moutet incapable to control a volley after over two and a half hours.
