Venus Williams of the U.S. (Photo: Reuters)
Jankovic had won her last four meetings on clay against Williams, but once the American heated up in the wake of a first-set rain delay on Wednesday, the Serbian couldn't stop her.
Jankovic served for the first set at 5-4, but Williams broke and never looked back.
By the time she won the second set she had reeled off nine games in a row, capping the match with a backhand winner down the line.
"I hadn't played her in a long time, so in the first set I was just finding my rhythm and getting used to any new patterns she might have," said Williams, playing on a wild card invitation as she tries to rebuild a ranking dented by a lengthy injury and illness layoff.
"In the second set everything started landing for me. I was moving forward and playing my aggressive game. Honestly, I don't know how it went that nicely for me. Everything just landed, and she hit a few errors, and that helped me a lot."
Third-seeded Marion Bartoli of France found the going much tougher, but persevered to get past Russian Vera Dushevina 6-2, 6-7 (3/7), 6-4 in a second-round match lasting more than three hours.
"The first game was 22 minutes long I think, so that set up the tone," Bartoli said. "The last two years I lost first round here, and I didn't want to lose again in the first set, so I really tried my hardest.
"I didn't play my best, but I just kept fighting and kept fighting and was able to win."
Bartoli, who snapped Victoria Azarenka's 26-match unbeaten streak when she downed the world number one en route to the semi-finals at Miami last week, was playing her first match after enjoying a first-round bye.
She next faces Slovenia's Polona Hercog, a 6-3, 6-2 winner over American Varvara Lepchenko.
Russian Nadia Petrova, the 13th seed, saved two match points en route to a 2-6, 7-6 (8/6), 6-2 victory over US veteran Jill Craybas, a qualifier.
"Compared to my previous match in the first round I didn't play as well, but I have to give credit to Jill, she played very well today," said Petrova, who next faces eighth-seeded Anastasia Pavlyuchenkova. "She wasn't making any errors from her side, so I had to take control of the match and move her around, and I think I made too many errors."
Sixth-seeded German Sabine Lisicki, who claimed her first WTA Tour title at Charleston in 2009, rallied to beat Czech Andrea Hlavackova 2-6, 6-3, 6-4.
Lisicki next faces Yaroslava Shvedova, who upset 12th-seeded Belgian Yanina Wickmayer 6-2, 7-6 (7/2).
In other matches, Galina Voskoboeva of Kazakhstan defeated Argentine qualifier Paula Ormaechea 6-2, 6-3 to set up a third-round clash with Samantha 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.
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