Jankovic, the 28th seed, beat the Czech world number two 3-6 7-5 6-4.
It marked the first time since 2009 that two-time Wimbledon winner Kvitova, 25, has failed to make at least the quarter-finals at the All England Club.
Jankovic, 30, will face 2012 finalist Agnieszka Radwanska in the last 16.
Kvitova had been in scintillating form heading into the match, coming through her first two rounds in a total of just 93 minutes.
Initially, it looked like she would continue that form against Jankovic as she won the first set 6-3 in a mere 35 minutes.
However, Jankovic did not give up and broke decisively in the 12th game, when Kvitova drove a forehand into the net.
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A tense final set went with serve until the 10th game when Kvitova was suddenly rattled, making a number of errors to go from 30-love up to trail 40-30 and give Jankovic her first match point.
Kvitova then struck the net with a backhand and Jankovic dropped to the floor as victory was confirmed.
Defeat for Kvitova leaves just Serena Williams, Maria Sharapova, Lucie Safarova and Caroline Wozniacki as the last remaining top 10 seeds heading into the second week.
World number five Wozniacki progressed by beating Camila Giorgi in straight sets.
Denmark's Wozniacki, who lost to Italian Giorgi at the 2013 US Open, took just 72 minutes to win the third-round match 6-2 6-2.
The former world number one will next play 20th seed Garbine Muguruza, who stunned 10th seed Angelique Kerber 7-6 (14-12) 1-6 6-2 to progress.
Kerber is a former Wimbledon semi-finalist but the German faced an opponent who has form when it comes to causing shocks, having beaten Serena Williams at last year's French Open.
Spaniard Muguruza, who had won just once in two previous Wimbledon visits, caught the eye when she came out on top of an epic first set, settling the tie-break with a drive volley before pressuring Kerber to hit a forehand wide.
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Kerber fought back in the second set but wobbled in the third, dropping her serve twice as Muguruza claimed an impressive scalp.
Sabine Lisicki's hopes of reaching a first Wimbledon final since 2013 were ended as the 18th-seeded German was beaten in straight sets by 15th seed Timea Bacsinszky. Lisicki could not cope with Bacsinszky as the Swiss won 6-3 6-2.
Bacsinszky's fourth-round opponent is Romania's Monica Niculescu, 27, who is through to the second week at Wimbledon for the first time after beating 23-year-old Czech player Kristyna Pliskova 6-3 7-5.
It is the second time in Niculescu's career that she has made it into the fourth round of a Grand Slam, after getting that far at the 2011 US Open.
Radwanska, 26, staged a second-set fightback to see off Australian Casey Dellacqua 6-1 6-4.
The Polish 13th seed made short work of Dellacqua in the first set, but found herself 4-0 down in the second before winning six straight games to progress.
Finally, American world number 21 Madison Keys also won in straight sets, overcoming Germany's Tatjana Maria 6-4 6-4.
Keys will play 122nd-ranked qualifier Olga Govortsova after the Belarusian beat Magdalena Rybarikova of Slovakia 7-6 (7-4) 6-3.
Defending champion Petra Kvitova suffered a shock early Wimbledon exit as former world number one Jelena Jankovic fought back to secure a third-round victory.