Frenchwoman Bartoli edged the first set before dropping the second and sending the late-night match at La Costa Resort and Spa into a thrilling decider.
But the world number 10, against a player ranked 17 places below her, eventually got the better of her opponent to justify her top seed status and move into the last four after two hours and 50 minutes of play.
"I'm frustrated and disappointed," said Jankovic. "I completely lost focus. It was so tough mentally and physically and my forehand let me down.
"I had the match under control and let it go. I let her come back, I messed up. When you're down you have to keep the focus."
In the day's other quarter-final action in California, second seed Dominika Cibulkova proved too strong for Urszula Radwanska of Poland, the Slovakian winning 6-4 6-4.
The world number 14 will meets Nadia Petrova for a place in the final.
Russian fourth seed Petrova was taken to three sets by home hope Varvara Lepchenko but sealed a 6-4 2-6 7-6(5) victory to book her spot in the semis.
Hercog lost the first set but ran out a 3-6 7-5 6-4 winner over the Bulgarian. She will face the winner of Mona Barthel’s quarter-final match against Sofia Arvidsson.
Half the second-round matches were also played on Friday, with rain decimating Thursday’s action.
Johanna Larsson surprised Anabel Medina Garrigues on a good day for the Swedes.
The 23-year-old, ranked just outside the world’s top 100, beat the third-seeded Spaniard 6-4 6-4 to move into the quarters.
Larsson overcame a first-set break in her victory, which was carried over from Thursday.
She next faces sixth seed Klara Zakopalova, the Czech hammering Colombia’s Mariana Duque 6-0 6-1 to progress.
In other second-round matches, there was victory for another Swede as Arvidsson beat Dutchwoman Arantxa Rus 6-4 7-5.
She faces Anastasia Pavlyuchenkova in the quarters.