Nineteen of Medvedev's 21 championships have been achieved on hard surfaces
A revitalized the Russian player won his initial title for over two years with a win over Frenchman Moutet in the Almaty Open title decider.
The Russian, a former world number one, has had a torrid season, achieving just one match at the Grand Slams and suffering a setback at the American major.
His varied form on the tennis tour - and issues with his serving in especial - resulted in him falling of the elite rankings and eventually splitting with former coach Gilles Cervara.
Presently collaborating with Thomas Johansson and his other coach, he has gradually advanced in the past month - peaking in a tightly fought competitive triumph over challenger Moutet.
It is his initial title after the Italian tournament and maiden on a hardcourt after March of the previous year.
Success also indicates he has secured twenty-one victories at twenty-one various events.
"It's the first time I am participating in a tournament with my children simultaneously, so to win a trophy is really nice," said tennis professional Daniil Medvedev.
"This championship is in honour of my younger daughter her name, because the initial championship I got when my child my daughter was born was for her."
Medvedev, the former major winner, had lost his past six title deciders, featuring in the German tournament earlier this year.
The player's defensive play style and frequent emotional displays on the playing surface had caused observers to wonder if his capacity to perform at the highest level was finished.
However the athlete has implemented adjustments in the last few weeks, attempting to advance forward and perform assertively, reinforced by an improved service.
He came back from a deficit in the initial set against the difficult Frenchman, securing four of the last five points to gain the advantage.
The competitors traded service breaks in the middle set before the Frenchman, striving for his maiden tour championship, took control to push for a final set.
Moutet rescued four early-game chances in a tight final set before the Russian secured a break to fifteen to secure the win.
Fittingly, the winner clinched the title with a rally at the net area, with his opponent incapable to control a return after over two and a half hours.