The 28-year-old Australian, who tasted success in South Carolina three years ago when she captured her sole career title at a WTA 250 event, recorded a 6-4 6-0 win in 76 minutes on Thursday (AEDT) over the 16th-seeded Ukrainian.
She will next face Greek third seed Maria Sakkari in her first tour-level quarter-final in almost two years.
World No.135 Sharma, a lucky loser in the final round of qualifying at the clay-court event, backed up her win over compatriot Arina Rodionova – her first WTA main-draw victory since July.
Sharma had more aces and double faults than her 39th-ranked opponent, lost her serve when leading 5-2 in the opening set but broke the 34-year-old six times in a convincing display.
Fourth seed and 2017 champion Daria Kasatkina rallied after getting shutout in the second set for a 6-3 0-6 6-1 victory over Ashlyn Kruger.
Also moving on is No.10 seed and Charleston resident Emma Navarro, the daughter of tournament owner Ben Navarro, who defeated qualifier Katie Volynets 6-1 6-1.
Earlier, Victoria Azarenka and Anhelina Kalinina both advanced to the third round.
Azarenka, seeded 12th, defeated Elisabetta Cocciaretto 6-1 6-2 while the 15th-seeded Kalinina ousted past champion Caroline Wozniacki 6-2 6-3.
"It was quite a long day," Azarenka said.
"I was happy to have it delayed an hour or so, I was a bit sleepy. But so happy we were able to get out there."
Wet weather slowed progress with players in the first matches not heading to play until 5:30pm local time.
With AAP.
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