Jankovic came into the tournament ranked No. 1 in the world despite never having won a Grand Slam tournament. Her French opponent quickly won the first set in 31 minutes then capped the biggest win in her career with a forehand winner down the line.
"I knew I could beat Jelena on a good day, it was just a matter of executing it, play the right shot at the right time and don't make too many mistakes," said Bartoli, whose 34 winners were twice as many as Jankovic.
"I just started slow," the Serbian said. "I was completely not moving my feet."
Also Sunday, Russian Dinara Safina, the third seed, fought off a pair of match points before a 6-2, 2-6, 7-5 win over 15th-seeded Alize Cornet of France; unseeded Jelena Dokic topped Alisa Kleybanova, 7-5, 5-7, 8-6, and seventh seed Vera Zvonareva beat fellow Russian Nadia Petrova, the 10th seed, 7-5, 6-4.