Another momentum shift in the third set looked like it nearly broke Djokovic's spirit. He yelled at his entourage in the stands and destroyed a racquet as he stared down a 1-4 deficit.
So badly did the top seed damage his equipment that a ballkid was called to sweep up the graphite shards that had splintered everywhere after the brutal assault.
Remarkably, that explosion of emotion kicked Djokovic back into gear. He won 16 of the next 19 points and demoralised Zverev by winning the third set.
The fourth was a slugfest as both players pulled out some astonishing groundstrokes in gruelling rallies that pushed them both to the limit.
Djokovic was still on edge, shouting at his team members again as he risked being forced into a deciding set. But the class that has netted him 17 major titles was on show as he displayed incredible mental and physical endurance to win a tiebreak and progress into the semi-finals after a war lasting three hours and 30 minutes.
The 33-year-old will face qualifier Aslan Karatsev in the semis after the unseeded Russian stunned the world by becoming the first player ever to qualify for the final four in their first appearance at a grand slam.
In the big match in the women's quarter-final draw, Williams was far too good for Simona Halep, blazing past the Romanian 6-3 6-3 to gain revenge and book her spot in the semifinals.
The 39-year-old came out all guns blazing against Halep, who thrashed the American 6-2 6-2 the last time they met at the 2019 Wimbledon final.
Williams thumped some seriously powerful winners off both wings to break for a 2-1 lead, before Halep broke back for 2-2.
The Romanian didn't have much joy after that though as Williams maintained the rage, winning the opening set in 36 minutes.
But the second set was full of twists and turns. Williams lost the plot briefly and made a stack of unforced errors, but Halep couldn't take full advantage.
There were four breaks of serve in the opening five games as Williams stayed in the hunt even though her level had dropped considerably from the first set.
But midway through the set Williams upped the ante. She overpowered Halep in some extraordinary baseline rallies and broke again, then consolidated on serve for a 5-3 buffer before sealing the result with yet another break.