Rising Canadian star Eugenie Bouchard, a semi-finalist at the Australian Open in January, continued her rousing run at the tournament as she ousted Jankovic 6-3 4-6 6-3 after a match lasting just over two hours.
Bouchard, who beat former world number one Venus Williams in the previous round, won five of the last six games to book her place in the final four, where she will meet Andrea Petkovic, the 14th seed.
"I knew in the second set my game wasn't where I wanted it to be," Bouchard told reporters.
"She (Jankovic) did a good job of stepping in and controlling, and she changes directions a lot, so I was really on the run.
"That's not where I want to be most of the time. I needed to get back to my game. I had to move forward. It was important to have short-term memory."
Germany's Petkovic, who ousted compatriot and 2009 champion Sabine Lisicki in the third round, advanced to the semi-finals with a 6-3 1-6 6-1 victory over Czech Lucie Safarova.
Also going through to the semi-finals was 17-year-old Swiss qualifier Belinda Bencic, who stunned third-seeded Errani 4-6 6-2 6-1.
Bencic, ranked 140th in the world, broke her opponent's serve seven times in the last two sets to reach her first WTA semi-final.
The quarter-final between Bouchard and Jankovic featured two of the most athletic movers in the women's game and the pair slugged it out with a dazzling display of marathon rallies and brilliant retrieving.
"I tried my best out there, but it just wasn't enough," Jankovic said, before praising her opponent.
"She's very solid. She stays so low and takes your balls so early off the ground, so even if you hit hard, she just picks them up so easily and kind of directs them. That's her biggest strength."
Bencic will meet Jana Cepelova after the Slovakian continued the upset theme by bouncing compatriot Daniela Hantuchova 6-2 6-1 in 74 minutes in the last quarter-final.
Ranked 78th in the world, Cepelova is searching for her first career title and won almost 70 percent of her first serve points to take out the 32nd ranked Hantuchova.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)