19 of the Russian's 21 victories have been earned on hardcourt
A comeback Medvedev won his maiden championship for over two years with a win over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has experienced a torrid period, achieving just a single victory at the Grand Slams and experiencing a difficult moment at the US Open.
His inconsistency on the professional circuit - and struggles with his serve in particular - resulted in him exiting of the top ten and ultimately parting ways with former coach Gilles Cervara.
Currently collaborating with Johansson and his other coach, Medvedev has consistently advanced in the last few weeks - climaxing in a tightly fought 7-5 4-6 6-3 victory over challenger Moutet.
This represents Medvedev's first championship since the 2023 Rome Masters and maiden on a hard court after March of that year.
Victory also signifies Medvedev has secured 21 titles at twenty-one distinct tournaments.
"This marks the first occasion I have attended a tournament with my children simultaneously, so to get a trophy is really nice," said ranked player Medvedev.
"This victory is in tribute of my younger daughter her name, because the maiden victory I achieved when my child my daughter was born was for her."
The tennis star, the 2021 US Open champion, had lost his previous six title deciders, comprising in Halle in the past months.
The player's counter-punching strategy and recurring outbursts on the playing surface had caused observers to doubt if his capacity to compete at the highest level was concluded.
But the 29-year-old has made changes in recent weeks, attempting to approach the net and play positively, reinforced by an better service.
The champion fought back from a break down in the opening set against the challenging Frenchman, winning four of the concluding five exchanges to go ahead.
Both players traded service breaks in the second set before Moutet, bidding for his first ATP Tour victory, seized the initiative to force a third set.
He saved four initial break points in a competitive third set before the champion secured a break to that score to secure the win.
Appropriately, Medvedev clinched victory with a point at the net, with his opponent unable to handle a volley after a lengthy match.