The eighth-seeded Spaniard took advantage of Ishizu's serve by breaking her on both opportunities in the first set, then breaking her serve four more times in the second set to advance.
Suarez Navarro, the only seeded player in action Tuesday, played in her first tournament since losing a tight two-setter to world No. 8 Petra Kvitova in the round of 16 at Wimbledon.
Qualifier Sesil Karatantcheva of Kazakhstan moved to the second round with a 6-5, 7-5 win over Germany's Julia Goerges. Karatantcheva is ranked 137th in the world, while Goerges is No. 42.
In other first-round matches, Poland's Ursula Radwanska was a 7-6 (3), 6-4 winner over qualifier Marina Erakovic of New Zealand, and qualifier Coco Vandeweghe advanced with a 6-1, 6-2 victory over wild-card entrant Allie Kiick, daughter of former Miami Dolphin running back Jim Kiick.