Mallory Burdette, runner-up in this year's NCAA singles championship and playing in her first WTA event, stormed to a 5-2 lead against Bartoli in the opening set.
Burdette, however, did not win another game as Bartoli rallied for a 7-5, 6-0 victory.
Bartoli reached the finals of this tournament last year before losing to Serena Williams and those two are on track to meet in the title match again this week.
In other second-round matches Thursday, Sorana Cirstea ousted Saisai Zheng 6-3, 6-3 and Urszula Radwanska was a 6-3, 3-6, 6-4 winner over Marina Erakovic.
Williams, coming off her Wimbledon championship, will take on Chanelle Scheepers in Friday's main quarterfinal attraction while Bartoli, the second seed, will meet Yanina Wickmayer.
2014: The Year in Music [PHOTOS]