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Barty moves on to the quarter-finals where she will face Spain's Paula Badosa, a 6-3, 6-3 winner over Caty McNally of the US.
"Shelby's an exceptional ball-striker, she always makes you work very hard for every single point, every single match, and tonight was no different," said Barty.
The Australian from Ipswich arrived in Charleston fresh off a victory in the prestigious Miami Open, where she successfully defended a WTA title for the first time.
After a first-round bye she made a quick adjustment to the green clay of Charleston, needing just 61 minutes to dispatch Japan's 77th-ranked Misaki Doi, 6-2, 6-1.
Unseeded Danka Kovinic of Montenegro, ranked 91st in the world, toppled two-time Wimbledon champion Petra Kvitova, the third seed, 6-4, 6-1 to reach the quarters.
"We both have pretty big serves and she's very good hitting from the baseline," Kovinic said. "Today it was the key that I tried, and did it really well, to take her pace of the ball and use her energy. As you can see, her returns on my second serve were sometimes incredible -- I didn't even move and the ball passed by me, but somehow I managed."
Kovinic broke twice for a 5-1 lead in the second set, then served out the victory with four straight service winners.
Kovinic will battle for a place in the semi-finals against Kazakhstan's Yulia Putintseva, who advanced when sixth-seeded Garbine Muguruza retired while leading their match 6-0, 2-2 with a left leg injury.
Muguruza fired 10 winners to Putintseva's one in the first set. She mustered a break of serve after a medical time out early in the second before opting to call it a day.
"I was already feeling some pain in my first match," said Muguruza, a former world number one who ended a two-year title drought in Dubai last month.
"The switch of hard courts to clay was tough, and in a very short amount of time. I started very well, and all of a sudden I felt a sharp pain in my leg, and it got worse," the Spaniard said. "I didn't want to continue without playing my best tennis. It didn't make sense to me."
US teen Coco Gauff booked a quarter-final meeting with Tunisia's Ons Jabeur. Gauff beat compatriot Lauren Davis 6-2, 7-6 (7/2) while Jabeur rallied for a 5-7, 6-3, 6-3 victory over France's Alize Cornet.
American Sloane Stephens, the 2016 Charleston champion, beat Australian Ajla Tomlmanovic 6-3, 6-4 to book a quarter-final clash with Russian Veronika Kudermetova, who downed Japanese qualifier Kurumi Nara 6-0, 6-3.