The 38-year-old fought past third seed Zverev 4-6, 6-3, 6-2, 6-4 in a night session duel, which captivated Court Philippe Chatrier over three-and-a-quarter hours.
Sixth seed Djokovic moves on to face world number one Jannik Sinner in the last four, after the Italian earlier raced past the unseeded Alexander Bublik in straight sets.
“Matches like this is one of the reasons I carry on playing and I love the competition,” said Djokovic.
On centre court, last year’s runner-up Zverev roared out of the blocks with a break of serve in the very first game.
That game proved the difference-maker as the only other break point generated in the entirety of the rest of the set was saved by the German as he served out the opener.
It was the first time former world number one Djokovic has dropped a set at the French Open this year.
But the 24-time major winner did not dwell on that fact.
The second set continued where the first had left off, until Djokovic engineered himself a 3-1 lead after Zverev pushed a backhand long when serving at 30-40.
The next game then produced just the second deuce of the match so far as both players began to make headway on the other’s service.
Djokovic eventually consolidated a crucial hold with an ace to end the game, which lasted nearly nine minutes.
The rest of the set continued like a mirror image of the first, with Zverev battling hard but being unable to muster up many break opportunities on Djokovic’s serve.
The set was sealed at the third time of asking as the three-time Roland Garros champion executed an immaculate backhand drop-shot to conclude a spectacular rally, replete with drop-shots, overheads and net cords.
The Serb sniffed out a break opportunity in game five of the third set and snaffled it after a couple of deuces with a delightful drop-shot to earn advantage, before Zverev planted a forehand in the tramlines.
With a player for the first time in the ascendancy in the match, Djokovic doubled his advantage when a Zverev volley dropped agonisingly long of the baseline, with his opponent stranded in the service box.
The sudden swing to Djokovic’s favour seemed to destabilise the 28-year-old as he started the next game with an attempted dropper that nestled in the bottom of the net as Djokovic moved into a 2-1 lead to love.
Still on a high, Djokovic started the fourth by again breaking the big-serving Hamburg-native.
He brought Chatrier to its feet when he whipped a cross-court forehand past Zverev to save break point in the sixth game at the end of an exchange that the 1.98m German looked certain to win on at least three occasions.
Zverev appeared a defeated man when he eventually passed up that chance at a vital break-back with a netted forehand.
Djokovic marched on and sealed his 101st win at the French Open, raising his arms aloft in triumph after finally converting match point at the fifth time of asking.
Defeat at the quarter-final stage of the tournament in which he has reached at least the last four every year since 2021 brings an end to a disappointing clay-court season for Zverev.
The three-time Grand Slam runner-up endured early exits at the Monte Carlo Masters and Madrid Open, as well as in the last eight in Rome. (AFP)
