The 28-year-old world No.135 recorded a 6-4 6-1 win in just 73 minutes.
Sharma, a lucky loser, took all four of her break-point opportunities and will next face 16th-seeded Ukrainian Lesia Tsurenko at the clay-court event.
Elsewhere on Wednesday (AEDT), Miami Open champion Danielle Collins and Sloane Stephens were among the first-round winners.
Collins, who has said this season would be her last because she's suffering from endometriosis, an ailment that affects the uterus, beat Spain's Paula Badosa 6-1 6-4.
"I'd rather like to go out with a bang, you know, than the other way," Collins said.
"I know everybody has a different way of ending their professional career, and for me I want to go out playing my best tennis."
Stephens, the 2017 US Open champion, defeated Poland's Magdalena Frech 6-0 6-2, on what she describes as her favourite surface.
"It's more athletic. It's more running, more sliding, just a lot more adversity I feel like, but in a good way," Stephens said.
"When you think the point is over, it's never over."
Other early victors included Taylor Townsend and third-seeded Greek Maria Sakkari, who claimed a 6-3 6-3 win over Viktoriya Tomova of Bulgaria.
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