World number two Kvitova had breezed through her first two matches of the tournament but after taking the first set against 30-year-old Jankovic, the Czech made too many errors allowing the 28th seed to triumph 3-6 7-5 6-4.
Kvitova, who won the Wimbledon title in 2011 as well as last year, was at a loss to explain how she had gone from a set and 4-2 up to losing a match that looked well within her control.
"Tough to explain. If I knew what happened, I would tell you. But I'm not really sure what happened out there. I was kind of up in the second set. Suddenly I felt like she's, you know, coming back, playing a little bit aggressive," said Kvitova.
"Suddenly from my side, I didn't have an answer for it. My serve didn't help me at all this time, as well. I was really struggling with each shot which I played."
Kvitova looked confident at the start, having dropped only three games in her first two matches, and when she broke Jankovic in the fourth game she looked set to progress.
The 25-year-old broke again in the third game of the second set on a sun-drenched court and went 4-2 ahead as Jankovic struggled to match her power.
But the experienced Serb had battled through two three-set matches already at the All England Club and knew how to dig deep as she fought back to 4-4 before forcing a decider.
The final set went with serve until Jankovic, who had begun to find the shots that saw her reach the U.S. Open final and top the rankings in 2008, broke Kvitova to close out the match.
"I am overwhelmed and so excited," said Jankovic, who has never been past the fourth round at Wimbledon.
"I have played so poorly the last couple of years and playing on Centre Court against the defending champion was unbelievable. The crowd was really great.
"I just tried to stay in there, stay positive and fight and I made it. I have to keep going... Beating Petra gives me a lot of confidence for the tournament."
In the last 16 Jankovic faces Poland's 13th seed Agnieszka Radwanska who beat Casey Dellacqua of Australia 6-1 6-4.
(Reporting by Ken Ferris, editing by Pritha Sarkar/Mark Meadows)
