It gave the top-seeded, 21-year-old Frenchman five career titles and eight in the last two seasons.
"It's my first title of the year and my first title in India," Gasquet said. "I didn't lose a set all week, which was very good (and) will have great memories of this tournament for sure."
Gasquet earned $65,850.
Rochus, the eight-seeded Belgian, was playing in his first final since winning the BMW Open in Munich last year.
"It was close," Rochus said. "I didn’t serve as well as I did in the previous match. Richard has a lot of experience and he never makes stupid errors. He makes you play and he makes you run."
Before Sunday, Rochus had lost in the first round of each of his three previous events since a quarterfinal appearance at the Swedish Open in July.