Two former champions also battled for supremacy in an ebb-and-flow classic on Centre Court.
It was 2011 title holder Petra Kvitova who prevailed 5-7 7-6(2) 7-5 in the contest of big servers against five-times champion and crowd favourite Venus Williams.
While you could barely separate Kvitova and Williams, champion Andy Murray soothed home nerves with a one-sided and danger-free win over Roberto Bautista Agut of Spain 6-2 6-3 6-2.
Australian Open champion Li faced fired-up Czech Barbora Zahlavova Strycova, who has never before advanced beyond the third round of a grand slam.
The pair fought a tight duel that could have gone either way, but the determined Czech held firmer in two tiebreaks to win 7-6(5) 7-6(5).
Tomas Berdych also came off second best in two tiebreaks as he lost a late-night thriller 7-6(5) 6-4 7-6(6) to Marin Cilic in a match that ended at 9.38pm local time – the latest finish at the All England Club outside of Centre Court.
The world number six was the highest men’s seed to fall and vented his frustrations by blaming officials for “making too many mistakes” and allowing the match to go on despite it being “too dark for Hawkeye to work”.
There were no such problems for the title favourites.
Djokovic was cantering towards a regulation victory against Frenchman Gilles Simon on Centre Court when, with the score at 6-4 6-2 3-2, he slipped before flinging himself at a forehand.
He fell heavily and rolled on the turf clutching his shoulder and grimacing in pain.
His coach Boris Becker, so demonstrative as a player, was a picture of calm inscrutability until Djokovic’s fall. The German three-times champion stood up, leaned forward and watched anxiously as his charge received treatment.
After some shoulder manipulation by his chair, the Serb resumed as if nothing had happened and finished off Simon 6-4 6-2 6-4 with a characteristically athletic airborne smash.
“It was a sharp pain when I fell, an awkward fall,” the six-times grand slam champion said.
“I was just hoping there is nothing going on with the joint. Luckily, there is no damage and I could play.”
Djokovic, who consulted a doctor and had an ultrasound scan to confirm there was no damage, was able to joke that he would take diving lessons from Becker, renowned for grasscourt acrobatics during his playing career.
The world number two will now meet France’s Jo-Wilfried Tsonga, another fine tumbler, in Monday’s fourth round.
Women’s third seed Simona Halep suffered a less spectacular scare, dropping a set against unheralded Ukrainian Lesia Tsurenko in a delayed second-round match.
Halep, who has vaulted up the rankings over the past year and reached the French Open final this month, eventually saw off the world number 170 6-3 4-6 6-4, but not before throwing away two match points as she struggled with her nerves.
“You know, on grass it is not easy. Every match is difficult. You never know who will win or who will lose because of the court,” Halep said.
Forecast rain failed to arrive at Wimbledon, preferring perhaps to dump on the Glastonbury Festival 200 km to the west, but a swirling wind made serving problematic at times.
The wind did not prevent Kvitova and the 34-year-old Williams from treating spectators to a top-class demonstration of fast and powerful grasscourt tennis.
Venus had Kvitova on the ropes for much of the match, punching groundstroke winners on both sides of the court. But the Czech sixth seed, who has failed to find the form she showed in the three years since her triumph, found fresh legs during the tiebreak.
A disappointed Williams, who has suffered debilitating illness in recent years, said she would now concentrate on the doubles with sister Serena and had no intention of quitting tennis.
“I’m not getting out of here. I think this year has been a great year for me. I’ve had some tough losses, but I’ve learned a lot from them … I’m proud of myself for what I’m achieving on the court.”
Third seed Murray produced an accomplished display of all-court tennis, triumphing on his fourth match point on his Spanish opponent’s serve in one hour 35 minutes.
“There were a few things I could do better but it’s been a good first week,” said Murray, who has yet to drop a set. After last year’s title and the Olympic success in 2012 Murray is now on a 16-match winning streak at Wimbledon.
Murray next meets 2.03-metre tall South African Kevin Anderson, who beat Italian Fabio Fognini.
“He’s a big guy with a big serve, so I’ll have to be sharp for that one,” Murray said.
Battling Australian Leyton Hewitt bowed out of the tournament he won in 2002 – a year when Venus was runner-up to Serena – but not before giving 15th seed Jerzy Janowicz a thorough workout in a second-round match held over from Thursday.
Pole Janowicz, beaten by Murray in the semi-finals last year, prevailed 7-5 6-4 6-7(7) 4-6 6-3 and will meet Spaniard Tommy Robredo in the third round.
He will be joined by compatriot and fourth seed Agnieszka Radwanska, who silenced Michelle Larcher De Brito, one of the noisiest grunters on the tour, 6-2 6-0.
It was Hewitt’s 42nd five-set grand slam match and gave the 33-year-old the record for most five-setters since the start of the professional era in 1968.
Queen’s Club champion Grigor Dimitrov, 10 years younger than Hewitt and with grand slam success in his sights, had to fight for his fourth-round spot in a 6-7(3) 6-4 2-6 6-4 6-1 tussle with Alexandr Dolgopolov.
The Bulgarian said his triumph in the Wimbledon warm-up event at Queen’s had given him extra hope and excitement after a five-set defeat last year.
“I’ve prided myself on some of the matches I’ve played so far. Some of my mental strength comes from that,” he said.
(Editing by David Goodman)