Nineteen of Medvedev's twenty-one titles have been won on hard courts
A comeback the Russian player won his maiden trophy for 882 days with a win over Frenchman Moutet in the Almaty Open final.
Medvedev, a former number one, has had a torrid season, winning just a single victory at the big events and experiencing a setback at the New York tournament.
Medvedev's unpredictability on the tennis tour - and issues with his service game in specific - resulted in him dropping out of the top ten and eventually separating with former trainer his previous coach.
Now training with Johansson and Goetzke, he has consistently progressed in the past month - culminating in a closely contested 7-5 4-6 6-3 win over Frenchman Corentin Moutet.
This marks Medvedev's maiden title after the Rome competition and first on a hardcourt after that period of the previous year.
Victory also indicates the Russian has achieved 21 championships at 21 various events.
"It's the first time I am participating in a event with my two daughters at once, so to win a championship is particularly special," said tennis professional the champion.
"This championship is in honour of my younger daughter my daughter, because the maiden victory I got when my older daughter my daughter was born was for her."
The tennis star, the former major winner, had failed in his last six finals, comprising in Halle in the past months.
The player's retrieving play style and recurring reactions on the tennis court had caused some to question if his capacity to perform at the elite level was over.
However the 29-year-old has made changes in the last few weeks, attempting to approach the net and compete assertively, supported by an better service.
The champion came back from a deficit in the initial set against the difficult Moutet, winning 4 of the last five exchanges to take the lead.
The pair exchanged service breaks in the following set before the challenger, attempting for his first tour victory, gained dominance to push for a final set.
He saved four early opportunities in a competitive final set before Medvedev won the break to that score to serve for the match.
Suitably, he clinched the title with a shot at the net, with the Frenchman failing to manage a shot after two hours and 38 minutes.
