The 19-year-old German's other title came last September when he beat three-time Grand Slam champion Stan Wawrinka to win the St. Petersburg Open in Russia.
This time, he denied Gasquet a 15th career title.
He broke the Frenchman's serve once in each set and made the decisive break in the eighth game of the second set, before serving out the match.
The fourth-seeded Zverev was solid against the third-seeded Gasquet, winning 80 percent of his points on first serve and hitting eight aces.
Zverev, the younger brother of tennis player Mischa Zverev, is considered one of the rising stars of the game and recently took 14-time Grand Slam champion Rafael Nadal to five sets in the third round of the Australian Open.
In October 2016, Zverev became the youngest player to enter the ATP top 20 since Novak Djokovic in 2006.