Mahut battled back from a first set loss to take a 5-7, 7-5, 6-3 victory over the 2012 runner-up Hewitt on center court.
Mahut breezed past American Michael Russell 6-2, 6-2 in the semis earlier on Sunday to reach the final and became the first Frenchman to claim the Newport title since Fabrice Santoro five years ago.
The 31-year-old improved to 2-2 all-time in title matches on the ATP Tour. He clinched his first career ATP title last month at ’s-Hertogenbosch.
Mumbai Roundup: 9 incidents that took place this week
Photos: Ajay Devgn, Parineeti, Tabu at 'Golmaal Again' trailer launch
Photos: Dipika Pallikal Karthik oozes oomph in bikinis and sarees
Photos: Kareena Kapoor Khan's grand birthday bash
Photos: 'Dangal' girls Sanya Malhotra, Fatima Sana Shaikh's dinner outing