The scores were 7-6 (9-7), 0-6, 6-1.
"This was a tough match and a great victory for me," Djokovic told the BBC. "The conditions were tough and so was Richard."
It was the third title this season for the 19-year-old Djokovic.
He won the Next Generation Adelaide International in Australia in January, and the Sony Ericsson Open in Miami April 1.
His second career victory over Gasquet was worth $100,000.
The fifth-seeded Gasquet was trying for his first title of 2007 and the fifth of his career. His last title came at Lyon, France, in 2006.
Notable deaths of 2014 [PHOTOS]