The two players, tied at 7-7 in head-to-head meetings ahead of the final, exchanged breaks early on in the first set, before the big-serving Czech prevailed 7-5 in a tiebreak.
The 31-year-old, who missed the U.S. Open after suffering from appendicitis, continued to heap pressure on Gasquet by securing an early break in the second set, but the third-seeded Frenchman saved two match points to level the contest through another tiebreak.
Playing in his 30th tour final, Berdych raced to a 5-3 lead without facing a break point in the deciding third set, and eventually held his nerve to secure the 13th ATP title of his career.
"Five weeks ago I was in hospital, now I'm sitting here with the trophy. Things are changing very quickly," Berdych said.
"Luckily for me, everything is going well, I'm feeling good, sitting here as a winner. I'm just taking all this as a bonus, that I can play and win some matches."
(Reporting by Nivedita Shankar in Bengaluru, editing by Pritha Sarkar)
