The French woman, who ended Victoria Azarenka's 26-match unbeaten run in 2012 in Miami last week, was playing her first match after a first round bye.

Bartoli breezed through the opening set and was quickly up a break in the second before the Russian rallied to level in a tie-breaker.

Bartoli finally pulled ahead in the third, winning consecutive games to move in front 5-3 before serving out for a 6-2 6-7 6-4 success.

"It was great to put up a fight and get the win out there," she said.

She next faces Slovenia's Polona Hercog, a 6-3 6-2 winner over American Varvara Lepchenko.

Sixth seed Sabine Lisicki was also made to work hard before the German pulled through against Czech qualifier Andrea Hlavackova, 2-6 6-3 6-4.

In other early matches, Galina Voskoboeva of Kazakhstan defeated Argentinian qualifier Paula Ormaechea 6-2 6-3 to set up a third-round clash with second seed Sam Stosur.

New Zealand's Marina Erakovic, seeded 17th, beat Georgia's Anna Tatishvili 7-5 6-3 to advance to a meeting with fifth-seeded American Serena Williams.