Nineteen of the Russian's 21 victories have been won on hard surfaces
A resurgent Medvedev claimed his initial trophy for nearly 30 months with a win over opponent Moutet in the Almaty Open championship match.
Medvedev, a former number one, has experienced a challenging year, achieving just one match at the big events and experiencing a setback at the American major.
Medvedev's unpredictability on the tennis tour - and difficulties with his serve in particular - led to him exiting of the world's top 10 and ultimately splitting with long-time mentor Gilles Cervara.
Now training with Thomas Johansson and Rohan Goetzke, he has consistently improved in the last few weeks - climaxing in a hard-fought competitive victory over Frenchman Moutet.
It is the player's first championship after the Rome competition and first on a hard court after March of the previous year.
Victory also indicates the Russian has achieved twenty-one championships at 21 different events.
"For the first time I am participating in a event with my children at once, so to win a trophy is especially meaningful," said world number 14 Daniil Medvedev.
"This championship is in dedication of my second daughter her name, because the initial championship I achieved when my child Alisa was born was for her."
The tennis star, the former major winner, had failed in his past six finals, comprising in Halle previously this season.
Medvedev's counter-punching approach and regular outbursts on the playing surface had prompted commentators to question if his skill to perform at the top level was finished.
However the player has implemented adjustments in recent weeks, attempting to advance forward and play positively, supported by an better serving game.
The champion recovered from a deficit in the opening set against the challenging Frenchman, taking four of the concluding five exchanges to go ahead.
The pair exchanged service breaks in the following set before the Frenchman, striving for his first tour title, took control to force a final set.
The opponent rescued 4 early break points in a close final set before Medvedev broke to that score to serve for the match.
Fittingly, Medvedev earned victory with a shot at the front of the court, with the Frenchman incapable to control a return after over two and a half hours.
