19 of Medvedev's twenty-one titles have been achieved on hard surfaces
A resurgent the Russian player secured his first championship for 882 days with victory over Frenchman Moutet in the Almaty Open final.
The athlete, a former number one, has had a torrid period, winning just one match at the Grand Slams and suffering a difficult moment at the US Open.
His inconsistency on the tennis tour - and issues with his serve in particular - led to him exiting of the elite rankings and finally separating with long-time mentor Gilles Cervara.
Currently training with Johansson and his other coach, he has steadily progressed in the recent weeks - culminating in a closely contested three-set triumph over opponent Moutet.
This marks Medvedev's first championship since the Rome competition and first on a hard court since spring of the previous year.
The win also indicates he has achieved twenty-one championships at twenty-one different competitions.
"This marks the first occasion I have attended a event with my both daughters at once, so to win a trophy is particularly special," commented world number 14 Medvedev.
"This title is in honour of my younger daughter her name, because the first title I achieved when my older daughter my daughter was born was for her."
Medvedev, the 2021 US Open champion, had been defeated in his previous six championship matches, featuring in the German tournament in the past months.
Medvedev's retrieving strategy and regular outbursts on court had prompted commentators to wonder if his capacity to play at the top level was finished.
But the athlete has altered his approach in recent weeks, striving to advance forward and perform assertively, reinforced by an enhanced service.
The champion recovered from a deficit in the first set against the challenging Moutet, taking 4 of the final five points to go ahead.
The competitors exchanged break points in the second set before Moutet, attempting for his maiden ATP Tour victory, took control to create a decider.
Moutet defended four early chances in a tight final set before Medvedev won the break to 15 to close out the victory.
Suitably, the winner secured the win with a point at the net area, with his opponent incapable to handle a return after over two and a half hours.