The 26-year-old Granollers overcame resistance from the Russian-born Zverev, who is ranked No. 190.
Zverev held his serve and saved six break points before Granollers finally broke him in the ninth game to take a 5-4 lead to take the first set. The 22nd-ranked Spaniard broke the German twice in the second to wrap up the match.
Nadal won a record seventh French Open championship on Monday after defeating top-ranked Novak Djokovic at Roland Garros.