The Serbian third seed won a battle of the fittest, finishing the stronger against 20-year-old Czech Lucie Safarova to claim a 5-7 7-6 (7-4) 6-2 victory in the pick of the women’s singles matches so far.
But it was a below-par performance from Jankovic, who had hardly broken sweat in her first two matches but was forced to toil for two hours and 35 minutes against an opponent labouring with a knee injury but defying the odds to push her all the way in an epic.
“It was a big battle out there,” admitted Jankovic. “At one point I was thinking ‘my God, is there any way out?’.
“I thought that my opponent played really well. She has nothing to lose so she was just swinging at the ball making some unbelievable shots.”
Jankovic dropped only four games in her first two matches and there was no early hint of an upset as she moved serenely into a 3-1 lead.
But the Safarova produced some inspired tennis, highlighted by some stunning backhands, to win the next three games to go in front and took the first set when her opponent double-faulted on set point.
The second set was just as closely fought and, as the rallies became more prolonged, they began to take their toll on the knee injury Safarova sustained in her second round win over Eleni Daniilidou.
The players’ stamina was further tested in the next game, a marathon affair in which there were no fewer than 11 deuces until Safarova, having saved four break points, won it at the seventh attempt.
Two backhand errors then proved costly for Safarova as she lost the tie-break 7-4 and allowed her more experienced opponent to level the match.
The third set went with serve until Safarova dropped her serve in the crucial sixth game.
A fifth double fault then gave Jankovic match point and she was a relieved woman when Safarova put a backhand wide on the next point to bring the epic match to a close.
Meanwhile Martina Hingis became another casualty of the graveyard of champions when she was bundled out of Wimbledon at the third-round stage by unseeded American Laura Granville.
The 1997 champion, who had to save two match points to get past British teenager Naomi Cavaday in the first round, lost 6-4 6-2 to the world number 77, her first defeat by the American.
It was all over in just 66 minutes as Hingis three times dropped her serve and failed to win a single break point.
Eighth seed Anna Chakvetadze was another notable casualty on day five, losing to rising star Michaella Krajicek in three sets.
Krajicek, the 18-year-old sister of former Wimbledon champion Richard, won 7-6 6-7 6-2 to reach the fourth round of a grand-slam event for the first time and will meet Granville for a place in the quarter-finals.
Elsewhere, second seed Justine Henin eased past Elena Vesnina, of Russia, 6-1 6-3.
Former champion Serena Williams was equally dismissive of Milagros Sequera, winning 6-1 6-0.
Meanwhile defending champion Roger Federer was in immaculate form as he powered past Marat Safin 6-1 6-4 7-6 (7-4).
Safin, on his least favourite surface, was outclassed in the first two sets but stretched the world number one in an absorbing third.
However, Federer edged the tiebreak to make it 51 straight wins on grass.
Andy Roddick survived a brief scare against Spain’s Fernando Verdasco before booking his place in the fourth round.
The American raced through the opening two sets in just 58 minutes, but the third seed had to come from a break down and save two set points before sealing victory in a third-set tie-break
Fernando Gonzalez became the highest men’s seed to exit this year’s Wimbledon after losing a five-set thriller to Serbia’s Janko Tipsarevic 6-3 3-6 6-3 4-6 8-6.