Jankovic, the tournament's seventh-seeded player, posted her first win over Bartoli this season after struggling against the 14th-seeded Frenchwoman in previous matches.
"When my thoughts are on the court, I play at another level," Jankovic said. "That wasn't the case in previous matches. Today, I controlled the match and didn't let her play her game."
Jankovic has lost to Bartoli twice this year, at the Australian Open and at Stanford. The former World No. 1 said she is much more focused now that some personal problems are behind her.
"A lot of things happened this year," Jankovic said. "My mother had surgery and my grandmother died, and that affects your game. Tennis becomes secondary because there are more important things in life than tennis, but now it's the end of the year and hopefully I can finish strong and make a good start to 2010."
With the top six seeds eliminated, Jankovic is the highest seeded player still in the $2 million tournament.
Top-ranked Dinara Safina of Russia, Venus Williams and French Open champion Svetlana Kuznetsova all lost their opening matches Monday after first-round byes.
Former world number one Maria Sharapova, 25th in the world following a lay off after shoulder surgery last October, was to play Iveta Benesova of the Czech Republic later Thursday.