On another sun-blessed day when former world No.1 Daniil Medvedev proved the biggest casualty, the two title favourites Djokovic and Jannik Sinner moved into the last-16, ever closer to another semi-final showdown, like last year's clash won by the Italian.
But seven-time champ Djokovic, who'd played his previous two matches under the late-evening roof on Centre Court and made it clear to organisers he wanted a daytime date at the 'outdoor' championships, got a rude shock in the sunshine from the dangerous, big-serving Frenchman.
Though he emerged victorious again, 7-5 6-4 1-6 7-6 (7-4), Djokovic's 105th singles win at Wimbledon, which brought him level at the top of the men's list with Roger Federer, proved harder work than expected.
In the third set, Rinderknech had been only two points away from handing Djokovic a 6-0 drubbing -- an indignity he's only suffered 12 times in his career -- but despite this 18-minute humbling, there was an inevitability about the 24-time grand slam champ regrouping in the fourth.
After winning the match with a brilliant diving volley at the end of a thrilling rally which left both men exhausted on the floor, the 39-year-old was in a jovial mood, suggesting to the crowd: "I propose a match-up between me and Roger for 106! Let's just stop it here and call Roger to come!"
After his fall in the opening match against Miomir Kecmanovic and a couple of tiebreaks to get past Nuno Borges, there were no such dramas this time for Sinner as he seemed to have moved smoothly into a new gear while beating American Jenson Brooksby 6-4 6-3 6-4.
"I'm very happy about the win," said the Italian. "I'm trying to improve every day, it's a small step forward today. I'm trying to get better if I want to go far in this tournament."
The champion will next face Japanese qualifier Shintaro Mochizuki, who ended the adventures of Spain's young new star Rafael Jodar, winning 1-6 7-6 (7-5) 6-4 6-4.
The 23-year-old Mochizuki clearly doesn't fancy his chances that much, suggesting that he might have to find some distracting tactics to unsettle the champ.
"I think he's just a celebrity for me," said the world No.151.
"He's going to try to destroy me. I just want to do whatever I can to, let's say, distract him -- because just by hitting tennis balls, I don't think I can beat him at all."
Shock of the day came with Russian eighth seed Daniil Medvedev, a former Wimbledon semi-finalist, being sunk 7-6 (7-4) 7-6 (7-5) 7-5 by the big-serving German veteran Jan-Lennard Struff, while Queen's Club finalist Tommy Paul was also a surprise casualty, losing to Poland's Hubert Hurkacz 4-6 7-6 (7-5) 7-5 6-2.
Jodar's fellow teenage star Joao Fonseca also bowed out 6-3 6-3 6-3 to Russian Roman Safiullin, who cracked 41 winners on the way to a last-16 clash with Djokovic.
