Sharapova cut short her campaign in September to recover from shoulder complaint. The fifth-seeded Russian, a semifinalist here last year, hit 23 winners against the unseeded Swiss player.
Bacsinszky broke Sharapova's serve early in the first set and went 2-0 up in the second set, but the Swiss player was also erratic with 11 unforced errors and four double faults.
Sharapova, a five-time Grand Slam champion, next faces 17-year-old Wang Xinyu. She defeated Xun Fang Ying 7-6 (3), 6-4 in an all-Chinese match.
Also in the first round, Ivana Jorovic of Serbia upset second-seeded Caroline Garcia of France 6-4, 6-2 and Alison Riske of the United States defeated No. 3 Wang Qiang of China 6-3, 6-3.
Russian players Veronika Kudermetova and Ekaterina Alexandrova, and Ons Jabeur of Tunisia also reached the second round.
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