The four-time Grand Slam champion has beaten Hantuchova nine straight times, with the Slovak's only win coming when they first played 10 years ago.
"I had a tough first opponent who can play extremely good tennis," Sharapova said. "I wanted to start the match off well. It was extremely important to put that pressure on her from the beginning. I think I did that really well today."
Sharapova hit 10 aces, saved all seven break points she faced, and broke Hantuchova's serve six times. She awaits eighth-seeded Kirsten Flipkens of Belgium or Yvonne Meusburger of Austria in the next round.
Kerber beat Klara Zakopalova of the Czech Republic 6-2, 7-5, while Pavlyuchenkova had a tougher time getting past seventh-seeded Carla Suarez Navarro 6-2, 3-6, 6-3.
In remaining first-round matches, there were two upsets as and Frenchwoman Kristina Mladenovic beat No. 5 Simona Halep of Romania, 7-6 (1), 6-4, and Elina Svitolina of Ukraine ousted sixth-seeded Roberta Vinci 6-3, 0-6, 7-5;