Stephens followed her teenage compatriot Taylor Townsend, who on Wednesday became the youngest player to go past the second round at Roland Garros since 2009 on the day world No.1 Serena Williams and her elder sister Venus were knocked out.
The 21-year-old Stephens blazed through the opening set before running into a spot of bother midway through the second as Hercog upped her game but the American ended the contest on her second match point with a crosscourt forehand winner.
"It was not easy, she is returning a lot of balls and the court is heavy and the conditions generally are heavy," Jankovic said.
"There are still a lot of great players in the draw, every round is going to be tough. The opponents get more and more difficult."
Former champion Svetlana Kuznetsova, the Russian 27th seed, laboured to a 7-6(5) 6-3 win over Italian Camila Giorgi to set up a meeting with either Czech fifth seed Petra Kvitova or New Zealand's Marina Erakovic.
Round 2 results:
4-Simona Halep (Romania) beat Heather Watson (Britain) 6-2 6-4
5-Petra Kvitova (Czech Republic) beat Marina Erakovic (New Zealand) 6-4 6-4
6-Jelena Jankovic (Serbia) beat Kurumi Nara (Japan) 7-5 6-0
15-Sloane Stephens (U.S.) beat Polona Hercog (Slovenia) 6-1 6-3
Julia Glushko (Israel) beat 21-Kirsten Flipkens (Belgium) 6-4 3-6 6-4
22-Ekaterina Makarova (Russia) beat Coco Vandeweghe (U.S.) 6-4 6-3
23-Lucie Safarova (Czech Republic) beat Casey Dellacqua (Australia) 6-1 5-7 6-3
Kiki Bertens (Netherlands) beat 24-Anastasia Pavlyuchenkova (Russia) 5-7 6-4 3-0 (Pavlyuchenkova retired)
26-Sorana Cirstea (Romania) beat Teliana Pereira (Brazil) 6-2 7-5
27-Svetlana Kuznetsova (Russia) beat Camila Giorgi (Italy) 7-6(5) 6-3
28-Andrea Petkovic (Germany) beat Stefanie Voegele (Switzerland) 6-2 4-6 6-2
Kristina Mladenovic (France) beat Alison Riske (U.S.) 7-6(5) 3-6 6-3
Paula Ormaechea (Argentina) beat Monica Niculescu (Romania) 2-6 7-5 6-2
Pauline Parmentier (France) beat Yaroslava Shvedova (Kazakhstan) 1-6 6-3 6-3
Maria Teresa Torro (Spain) beat Magdalena Rybarikova (Slovakia) 6-2 2-6 6-2
Silvia Soler Espinosa (Spain) beat Yanina Wickmayer (Belgium) 6-2 6-4
Follow the French Open on up to 7 courts LIVE on the Eurosport Player!
- Sports & Recreation
- Jelena Jankovic