The victory was additionally sweet for Kerber, who was looking for revenge after the Japanese teenager knocked her out of the U.S. Open in straight sets.
"It's always tough to play against her," Kerber said. "I was trying to come out here and really focus on every single point and make it better than last time. ... She's a great player and a tough opponent. For sure she will have great success in the future."
Osaka lost to Caroline Wozniacki in the final of last year's tournament
Kerber will play either Madison Brengle or Daria Kasatkina in the next round.
Also, wild card Kurumi Nara of Japan overcame a slow start to oust Yulia Putintseva of Kazakhstan 2-6, 6-4, 6-2, while China's Wang Qiang beat Kristina Mladenovic of France 6-0, 6-0.
Meanwhile, organizers announced that Agnieszka Radwanska, a two-time tournament champion, has pulled out due to a virus. The 11th-ranked Pole was seeded sixth.