19 of the Russian's 21 titles have been achieved on hardcourt
A comeback the Russian player claimed his initial title for nearly 30 months with a win over Frenchman Moutet in the Almaty Open championship match.
The athlete, a ex- number one, has had a difficult season, achieving just one match at the major tournaments and experiencing a difficult moment at the New York tournament.
His unpredictability on the ATP Tour - and issues with his serve in particular - resulted in him falling of the world's top 10 and finally parting ways with former trainer his previous coach.
Presently working with Thomas Johansson and Goetzke, Medvedev has consistently progressed in the last few weeks - culminating in a closely contested 7-5 4-6 6-3 triumph over Frenchman Moutet.
This represents his initial championship since the Rome competition and first on a hardcourt since spring of that year.
The win also indicates Medvedev has achieved 21 victories at 21 different events.
"For the first time I have attended a event with my both daughters together, so to secure a title is really nice," commented world number 14 the champion.
"This championship is in honour of my child Victoria, because the maiden victory I won when my first daughter my daughter was born was for her."
The tennis star, the 2021 US Open champion, had failed in his last six title deciders, including in Halle in the past months.
Medvedev's retrieving play style and recurring outbursts on the playing surface had led some to wonder if his skill to compete at the highest level was concluded.
But the player has altered his approach in recent weeks, attempting to come to the net and perform aggressively, reinforced by an improved serve.
Medvedev came back from a disadvantage in the initial set against the challenging Moutet, taking four of the concluding five points to gain the advantage.
The pair swapped breaks in the following set before the Frenchman, striving for his first ATP Tour title, seized the initiative to create a third set.
Moutet rescued four initial chances in a tight final set before Medvedev won the break to 15 to secure the win.
Fittingly, he earned the win with a point at the front of the court, with his opponent unable to control a volley after two hours and 38 minutes.