19 of Medvedev's 21 victories have been achieved on hardcourt
A comeback Medvedev claimed his initial title for over two years with success over Frenchman Moutet in the Almaty Open title decider.
Medvedev, a former world number one, has experienced a challenging season, winning just one match at the Grand Slams and undergoing a meltdown at the US Open.
The player's unpredictability on the ATP Tour - and struggles with his service game in especial - caused him dropping out of the top ten and eventually separating with former coach Gilles Cervara.
Presently collaborating with Thomas Johansson and Goetzke, Medvedev has steadily progressed in the recent weeks - climaxing in a hard-fought competitive win over opponent Corentin Moutet.
It is the player's initial trophy since the Italian tournament and first on a hard surface after March of the previous year.
Success also indicates Medvedev has achieved 21 victories at 21 distinct competitions.
"For the first time I am participating in a event with my both daughters at once, so to win a title is particularly special," said world number 14 Medvedev.
"This victory is in dedication of my second daughter Victoria, because the first title I achieved when my older daughter Alisa was born was for her."
The athlete, the past champion, had lost his past six title deciders, including in the German tournament earlier this year.
His retrieving strategy and frequent emotional displays on court had led some to wonder if his ability to compete at the highest level was concluded.
However the athlete has made changes in recent weeks, making an effort to come to the net and perform assertively, supported by an better serve.
The champion came back from a break down in the initial set against the difficult Moutet, securing 4 of the concluding five games to gain the advantage.
Both players traded service breaks in the following set before the Frenchman, attempting for his first professional victory, gained dominance to push for a final set.
He defended four initial break points in a tight final set before the champion secured a break to that score to secure the win.
Fittingly, the winner clinched the title with a shot at the net, with the Frenchman failing to control a shot after two hours and 38 minutes.