Leading by two sets and 3-2 in the third set, the Serb top seed was closing in on an uneventful victory against his French opponent when he stumbled and dived to reach a wide forehand, crashing heavily to the ground near the baseline.
With the 2011 champion in agony and with concerned coach Boris Becker watching on, it looked as though Djokovic might be out for the count but after receiving some treatment he carried on and closed out a 6-4 6-2 6-4 win.
Despite looking a little tentative, he showed no obvious signs of discomfort and finished the job with a hefty smash.
The shaken 27-year-old, who had slipped several times during a match featuring some long baseline exchanges, looked relieved at the finish and even more so later when the All England Club medical doctor gave him the all-clear.
"Luckily for me it was only an impact that had a minor effect on the joint and the muscles around, but no significant damage that can cause a bigger problem," Djokovic, who will face dangerous Frenchman Jo-Wilfried Tsonga, told reporters.
"I just came from the doctor's office, had ultrasound. It's all looking good."
While arguably the best mover in men's tennis, Djokovic said he may have to practise his diving with three-times champion Becker, who virtually trademarked the art during his golden years at the All England Club.
"It was obviously a scary fall. I talked with Boris. We obviously need to work on my diving volleys, learning how to fall down on the court. I'm not very skilful in that."
While he could joke about it later, Djokovic said when he felt a sharp pain in his shoulder he feared his Wimbledon might have been over.
"I tried to land on my left arm. I basically had a strong impact on the shoulder. When I stood up I felt that click or pop, whatever you call it. I feared maybe it might be a dislocated shoulder."
Djokovic has not lost before the quarter-finals at Wimbledon since 2008 and while not hitting top gear so far this year, he appears to have plenty in reserve.
He seemed content to trade shots from the baseline with the nimble Simon in the opening set, the two players apparently having the tennis equivalent of a staring contest as they pinged groundstrokes from corner to corner.
Simon blinked first, dropping serve to trail 4-2 but Djokovic then lost his own in the next game when his touch let him down with an attempted half-volley dropshot.
Simon held serve after eight deuces in a brutal eighth game but the effort he put in to restore parity told a couple of games later when Djokovic broke again to take the opener.
The match then looked like a foregone conclusion until the late drama in the third set.
Djokovic will now get the weekend to recover from his fall before playing 14th seed Tsonga, who he beat in the 2011 semis on the way to lifting the trophy for the only time.
"I think it's going to be fine," he said. "Anyway, they told me usually in these kind of particular cases you might feel soreness in the next couple of days.
"But I can play around with practices and recovery and see how it goes. But I'm quite confident it's going to be all right."
He will need to be firing on all cylinders on Monday against a player he says "can beat any one".
"I don't fear anything," Djokovic, who is in defending champion Andy Murray's half, said.
"He's a very aggressive player. If he's on, if he feels good on the certain day, he can beat anybody really.
"Going back a few years ago, playing semi-finals against him, 2011, I remember that match well, and also the Olympic Games. I won both of the matches but I know what threat he can cause on this surface."
Nothing went right for the sixth-ranked Czech as he became the highest men's seed to fall by the wayside in a match that finished at 9.38pm local time - the latest finish at the All England Club outside of Centre Court.
Croatia's Cilic admitted "it was very, very dark in the tiebreak" and Andy Murray observed that he could not "imagine what it was like for them" as he "couldn't see the ball on the TV".
Berdych, on the other hand, was angry with the lack of light, angry with a linesman for constantly making the wrong calls and angry that they were forced to play on even though technology had given up the ghost.
"I lost all the will to talk to that guy anymore," the 2010 Wimbledon runner-up told reporters.
"I saw so many mistakes from him. I ask him (the umpire) three times to change the guy. All he said (was) 'No, everybody can make mistakes. He's a great linesman. He's doing a great job, so give him a chance'.
"I said, 'all right, give him a chance. It's your call. I already lost two games (because of the linesman's wrong calls). Great'," he added sarcastically.
"Then the end of the match basically there was a third call, and then I look at the line... and there was the same guy. He (the umpire) just put him on another line."
To make matters worse, when Berdych wanted to challenge the call, he was told that was not an option because Hawkeye had stopped working due to the gathering gloom.
"He (the umpire) just told me, Hawkeye doesn't work because it's too dark. If... some machine doesn't work because we don't have enough light, then why do we have to play?" questioned Berdych.
"I didn't even have the energy to talk to him when we should stop... I just lost all the will to talk to him anymore."
Berdych had some sympathy from champion Murray, who has enjoyed some late-night blockbusters at Wimbledon that have stretched on till 11pm local time but at least those were under a floodlit closed Centre Court roof, rather than on Court Three.
"From a player's perspective, when the light starts to go, it's tough to play good tennis, to play properly," said the third seed.
"I don't think you want matches to be decided on someone shanking a ball because they can't see it. You want players to be able to play their best tennis for as long as possible.
"If it was too dark to see, then they should have stopped."
Wimbledon round three results
3-Andy Murray (Britain) beat 27-Roberto Bautista (Spain) 6-2 6-3 6-2
26-Marin Cilic (Croatia) beat 6-Tomas Berdych (Czech Republic) 7-6(5) 6-4 7-6(6)
11-Grigor Dimitrov (Bulgaria) beat 21-Alexandr Dolgopolov (Ukraine) 6-7(3) 6-4 2-6 6-4 6-1
14-Jo-Wilfried Tsonga (France) beat Jimmy Wang (Taiwan) 6-2 6-2 7-5
Jeremy Chardy (France) beat Sergiy Stakhovsky (Ukraine) 6-3 6-7(4) 6-3 6-0
15-Jerzy Janowicz (Poland) beat Lleyton Hewitt (Australia) 7-5 6-4 6-7(7) 4-6 6-3
19-Feliciano Lopez (Spain) beat Ante Pavic (Croatia) 6-4 7-6(4) 7-5
Santiago Giraldo (Colombia) beat 30-Marcel Granollers (Spain) 4-6 7-6(2) 1-6 6-1 7-5
- Sports & Recreation
- Tomas Berdych
- Boris Becker