Nineteen of the Russian's 21 victories have been earned on hardcourt
A comeback Medvedev secured his first championship for over two years with success over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has had a challenging season, achieving just one win at the Grand Slams and undergoing a difficult moment at the American major.
His unpredictability on the tennis tour - and issues with his serve in particular - resulted in him exiting of the elite rankings and finally separating with former mentor Gilles Cervara.
Presently training with Thomas Johansson and Rohan Goetzke, he has steadily progressed in the recent weeks - peaking in a hard-fought 7-5 4-6 6-3 triumph over opponent Corentin Moutet.
It is his first title following the Rome competition and initial on a hard court from that period of that year.
The win also indicates he has achieved twenty-one titles at twenty-one distinct events.
"This marks the first occasion I am participating in a competition with my both daughters together, so to win a championship is particularly special," said world number 14 the champion.
"This championship is in tribute of my child her name, because the maiden victory I achieved when my older daughter her name was born was for her."
The athlete, the former major winner, had lost his previous six title deciders, featuring in that event previously this season.
His counter-punching strategy and recurring emotional displays on court had led commentators to question if his skill to compete at the highest level was finished.
Yet the athlete has altered his approach in the past month, attempting to advance forward and play positively, backed up by an improved service.
The champion came back from a disadvantage in the first set against the tricky Moutet, securing 4 of the last five exchanges to take the lead.
The competitors traded break points in the second set before the challenger, striving for his maiden ATP Tour victory, took control to push for a final set.
Moutet defended four early-game chances in a tight third set before the champion won the break to 15 to secure the win.
Fittingly, the winner earned victory with a rally at the net area, with Moutet failing to manage a shot after a lengthy match.
