19 of the Russian's twenty-one victories have been earned on hard surfaces
A comeback the Russian player won his initial championship for 882 days with success over Frenchman Moutet in the Almaty Open final.
Medvedev, a ex- top-ranked player, has experienced a torrid season, managing just one match at the Grand Slams and suffering a difficult moment at the American major.
His inconsistency on the tennis tour - and struggles with his serving in especial - led to him dropping out of the world's top 10 and finally parting ways with former trainer Gilles Cervara.
Now collaborating with Thomas Johansson and his other coach, Medvedev has steadily advanced in the last few weeks - climaxing in a tightly fought three-set win over challenger Moutet.
It is his maiden trophy after the 2023 Rome Masters and first on a hard court from spring of that year.
Success also indicates the Russian has achieved 21 championships at 21 various events.
"It's the first time I'm at a competition with my children simultaneously, so to win a title is particularly special," commented ranked player the champion.
"This title is in dedication of my younger daughter her name, because the initial championship I achieved when my older daughter her name was born was for her."
The athlete, the 2021 US Open champion, had been defeated in his previous six title deciders, featuring in the German tournament earlier this year.
The player's defensive strategy and regular outbursts on court had caused observers to wonder if his capacity to perform at the top level was over.
Yet the player has altered his approach in recent weeks, making an effort to advance forward and perform aggressively, backed up by an improved serve.
He fought back from a break down in the initial set against the tricky Moutet, taking four of the final five points to go ahead.
Both players traded break points in the middle set before Moutet, attempting for his initial ATP Tour victory, took control to push for a final set.
He saved four initial opportunities in a close third set before Medvedev secured a break to that score to secure the win.
Suitably, Medvedev secured the win with a shot at the net area, with his opponent unable to handle a volley after over two and a half hours.