Granollers, who won the title in 2008, beat No. 5 seed Fritz, who reached the semifinals last season, for his second tour-level victory this season.
Ryan Harrison beat 40-year-old Ivo Karlovic, who won the title in 2007, 6-3, 6-4.
Casper Ruud defeated Hugo Dellien 7-6, 6-4, Christian Garin beat Pablo Cuevas 4-6, 6-4, 6-2 and Bernard Tomic defeated Denis Kudla 7-6, 7-5 in the rest of the first-round singles action.
In doubles play, Austin Krajicek and Artem Sitak defeated Lleyton Hewitt and Jordan Thompson 6-2, 4-6, 10-8.
Play continues on Tuesday.