Nineteen of the Russian's 21 championships have been won on hard courts
A revitalized the Russian player won his first title for over two years with success over Frenchman Moutet in the Almaty Open final.
The Russian, a ex- top-ranked player, has had a torrid season, managing just one match at the big events and experiencing a setback at the American major.
His inconsistency on the ATP Tour - and issues with his service game in especial - resulted in him dropping out of the top ten and finally splitting with long-term trainer his previous coach.
Currently working with Thomas Johansson and Rohan Goetzke, Medvedev has consistently progressed in the recent weeks - peaking in a tightly fought 7-5 4-6 6-3 win over challenger Moutet.
It is his first trophy following the Italian tournament and maiden on a hardcourt from spring of that year.
Victory also indicates Medvedev has won 21 titles at twenty-one different competitions.
"It's the first time I'm at a tournament with my two daughters at once, so to get a trophy is particularly special," said world number 14 Medvedev.
"This championship is in honour of my second daughter Victoria, because the maiden victory I got when my first daughter Alisa was born was for her."
Medvedev, the former major winner, had failed in his past six finals, featuring in Halle earlier this year.
The player's defensive strategy and regular outbursts on the tennis court had led commentators to wonder if his ability to compete at the top level was over.
However the player has altered his approach in the last few weeks, making an effort to approach the net and compete positively, reinforced by an better serving game.
He fought back from a deficit in the initial set against the tricky Frenchman, securing 4 of the last five points to gain the advantage.
The competitors traded break points in the second set before Moutet, attempting for his initial ATP Tour victory, gained dominance to create a decider.
He rescued four early-game chances in a close deciding set before the Russian secured a break to 15 to serve for the match.
Suitably, Medvedev clinched the win with a point at the front of the court, with Moutet failing to control a shot after over two and a half hours.
