In stifling conditions, the 54th-ranked Frenchman came back from a set down to stun an increasingly rattled Zverev into submission.
The German had injured his big toe towards the end of his last match in Shanghai but on Monday seemed to show no sign of discomfort as he broke Rinderknech in the third game with a forehand.
He nearly went ahead early in the second set, but Rinderknech recovered his cool, piling on the pressure in the fourth game to eventually break.
“I’m not very sure (how I managed to turn the game around),” he said.
“I fought like hell, tried everything. (Zverev) is such a good player… I knew it was going to be a battle.
“Starting in the second set… I was able to be offensive at the right moment, in a smarter way,” he said.
Keeping up the momentum, in the third set the 30-year-old broke in the third game.
Zverev had to pause to change his shoes because sweat was pouring out of them, as spectators wafted fans and wore cool packs on their foreheads to counter the suffocating humidity.
But switching footwear was not enough to save the German, and a double fault in the seventh game led to Rinderknech breaking again.
Holding with an ace to win, the Frenchman lolled his body in delighted disbelief, then danced around the court in glee.
Zverev’s exit means world number five Djokovic, who is aiming for a record-extending fifth title in the Chinese financial hub, now leads rankings-wise as the tournament heads into the last 16.
On Sunday, the competition lost both defending champion Jannik Sinner, who was forced to retire with extreme leg cramps, and fourth-ranked Taylor Fritz.
World number one Carlos Alcaraz withdrew at the last minute to rest.
Alex de Minaur is the next highest seed after Djokovic through to the fourth round, comfortably getting past Poland’s Kamil Majchrzak 6-1, 7-5.
“I came into this week knowing how tough the conditions were going to be,” the world number seven said.
“So the mindset ultimately is surviving, finding ways, and getting ready for battles every time you step out on the court.”
The Australian will next meet Portugal’s Nuno Borges, who put an end to the hopes of home favourite Shang Juncheng 7-6(5), 4-6, 6-3.
