Rising Canadian star 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.
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."
Big-hitting Pliskova thundered down 10 aces as she also raced into a 2-0 lead in the second set before Wozniacki’s ground strokes to the fore.
"It was particularly difficult to deal with her serve - she was serving very well and playing very aggressively," Wozniacki said.
"On these fast courts it wasn't easy, and getting breaks was difficult tonight, but I'm happy to be through. I'm especially pleased with how I played in the third set”
Ivanovic came through topsy-turvy match to beat Magdalena Rybarikova 6-1 0-6 6-2.
Having bageled Ivanovic in the second set, Rybarikova fell away in the decider as Ivanovic broke her counterpart in the first game of the set before winning with ease.
Kimiko Date-Krumm and Jovana Jaksic will contest the other semi-final.
Date-Krumm beat eighth-seed Monica Puig in two hours and 27 minutes 6-4 6-7 (2) 6-4; while 20-year-old Jaksic's match was a far more comfortable affair as she dispatched Julia Boserup 6-3 6-0.
Family Circle Cup Women's Singles quarter-finals
6-Eugenie Bouchard (Canada) beat 2-Jelena Jankovic (Serbia) 6-3 4-6 6-3
Belinda Bencic (Switzerland) beat 3-Sara Errani (Italy) 4-6 6-2 6-1
14-Andrea Petkovic (Germany) beat 9-Lucie Safarova (Czech Republic) 6-3 1-6 6-1
Jana Cepelova (Slovakia) beat Daniela Hantuchova (Slovakia) 6-2 6-1
Monterrey Open Women's Singles quarter-finals results
2-Ana Ivanovic (Serbia) beat 6-Magdalena Rybarikova (Slovakia) 6-1 0-6 6-2
3-Caroline Wozniacki (Denmark) beat Karolina Pliskova (Czech Republic) 6-7(3) 6-3 6-3
Jovana Jaksic (Serbia) beat Julia Boserup (U.S.) 6-3 6-0
Kimiko Date-Krumm (Japan) beat 8-Monica Puig (Puerto Rico) 6-4 6-7(2) 6-4
- Sports & Recreation
- Andrea Petkovic
- Ana Ivanovic
- Caroline Wozniacki
- Sara Errani