19 of Medvedev's 21 titles have been won on hardcourt
A comeback the Russian player won his maiden trophy for nearly 30 months with victory over Frenchman Moutet in the tournament final.
The Russian, a ex- top-ranked player, has endured a torrid season, winning just one win at the big events and experiencing a meltdown at the American major.
Medvedev's varied form on the tennis tour - and issues with his serving in particular - caused him exiting of the world's top 10 and eventually separating with long-time mentor Gilles Cervara.
Now training with his coach and his other coach, the tennis star has consistently advanced in the recent weeks - peaking in a closely contested three-set victory over opponent Moutet.
It is Medvedev's initial championship following the Italian tournament and maiden on a hardcourt since that period of that year.
Success also indicates the Russian has secured 21 victories at 21 various competitions.
"This marks the first occasion I have attended a event with my both daughters simultaneously, so to get a trophy is particularly special," commented tennis professional Medvedev.
"This championship is in tribute of my second daughter her name, because the maiden victory I got when my older daughter her name was born was for her."
The athlete, the past champion, had lost his past six finals, comprising in Halle earlier this year.
His defensive approach and recurring outbursts on the tennis court had led some to doubt if his ability to perform at the highest level was over.
However the player has made changes in the past month, striving to approach the net and perform aggressively, supported by an enhanced serving game.
The champion fought back from a deficit in the opening set against the tricky opponent, securing four of the concluding five exchanges to go ahead.
Both players exchanged breaks in the following set before Moutet, bidding for his maiden tour championship, gained dominance to create a decider.
Moutet saved four early break points in a competitive deciding set before Medvedev won the break to 15 to serve for the match.
Fittingly, the winner earned victory with a shot at the net area, with Moutet failing to handle a volley after over two and a half hours.
