Venus Williams also was upset in quarter-final action at the $600,000 claycourt event, but top seed and defending champion Nadia Petrova restored order with a 6-4 7-5 win over fellow Russian and fifth seed Dinara Safina.
Petrova will next face Sybille Bammer after the Austrian felled Slovak Hantuchova 2-6 6-2 6-2.
Williams, Jankovic and Hantuchova had all been heavily fancied to reach the semis but were stunned by free-hitting opponents.
Williams lost to eighth seed Tatiana Golovin of France 6-2 6-3 while Jankovic, a Serbian ranked ninth in the world, fell to number six seed Ana Ivanovic 7-5 6-3.
"Today was just one of those bad days when everything was wrong," said Jankovic. "I played terrible and made so many unforced errors."
Jankovic had little success in handling the blistering forehands of Ivanovic in a match in which neither Serb played particularly well.
TOO MANY MISTAKES
Ivanovic put just over half of her first serves in play while Jankovic won less than half the points off her first serve.
"I think for both of us it was not a good match," Jankovic said. "She was a little bit luckier at some times and I made too many mistakes."
Ivanovic who hit more double faults (seven) than aces (six) saved her best serving for the final game when she closed out the match with three consecutive aces.
"I did not have good success with my serve, but at the end, my serve helped me which was very important," said Ivanovic. "I was happy with my performance except there were times I should have been more aggressive."
Williams never got on track in losing to 20th-ranked Golovin for the second time in as many matches. After dropping the first set, Williams trailed 4-0 in the second before mounting a brief comeback by winning three consecutive games.
But Golovin broke Williams's serve in the next game and then held serve to clinch the triumph.
"We were back on serve so that was nice," said Williams who was playing in just her third tournament this year. "But those last two games went a lot quicker than I wanted them to."
Golovin was thrilled. "I put a lot of pressure on her right from the start," she said. "I was getting everything back. She kind of came back and I fought through that.
"It was one of the better matches I've played all season so I'm really happy."
Bammer seemed to wear down Hantuchova in the match that took two hours, eight minutes to complete. Bammer was only able to convert five of 17 break opportunities but it was enough to knock out the world's 14th-ranked player.
Golovin will meet Ivanovic in one of Saturday's semifinals with Bammer taking on Petrova.
