Former champion Svetlana Kuznetsova of Russia also advanced on Day 5.
The Serbian star Jankovic eased past Japan's Kurumi Nara 7-5, 6-0, while the 27th-seeded Kuznetsova, who captured the 2009 Roland Garros title and was the runner-up in 2006, defeated rising Italian Camila Giorgi 7-6 (7-5), 6-3.
American Sloane Stephens, seeded 15th, dropped only four games in a 6-1, 6-3 victory over Slovenian Polona Hercog.
In other action involving seeds, Israeli Julia Glushko took out No. 21 Belgian Kirsten Flipkens 6-4, 3-6, 6-4, No. 23 Czech Lucie Safarova got past Aussie Casey Dellacqua 6-1, 5-7, 6-3 and Dutchwoman Kiki Bertens knocked out No. 24 Russian Anastasia Pavlyuchenkova 5-7, 6-4, 3-0, retired.
Also on Thursday, Spaniard Silvia Soler-Espinosa dropped Belgian Yanina Wickmayer 6-2, 6-4; France's Pauline Parmentier overcame Kazakhstan's Yaroslava Shvedova 1-6, 6-3, 6-3; Argentine Paula Ormaechea came back to best Romanian Monica Niculescu 2-6, 7-5, 6-2; and Spaniard Maria-Teresa Torro-Flor held off Slovak Magdalena Rybarikova 6-2, 2-6, 6-2. Soler-Espinosa was a runner-up in her first-ever WTA final last week in Strasbourg, France.