In his first ever Masters 1000 final, 22-year-old Fils will play the winner of the all-American semi-final clash between Brandon Nakashima and Frances Tiafoe.
Fils beat the Roland Garros finalist from Italy for the third time in their career series to become the youngest French Masters finalist since a 20-year-old Richard Gasquet in Toronto two decades ago.
Cobolli struck first as he broke Fils for a 2-1 lead on a double-faults but immediately lost his own service game to love as the Frenchman levelled, 2-all.
The Italian went down for a second time, with his opponent catching the corner to take a 5-3 lead and serve out the next game with a concluding winner after 25 minutes.
Fils broke to start the second set as his intensity increased and he closed out the win with a stinging forehand winner to the corner past Cobolli.