The first set was a topsy-turvy affair, with both players quickly into their groove on serve before a succession of breaks.
Isner, whose hopes of reaching the semi-finals required a straight-sets win and a Djokovic victory over Cilic, netted a forehand to drop the set and there was only ever likely to be one outcome after that.
As in 2014, the first seven singles matches of the tournament have been completed in straight sets.
In stark contrast to second seed Roger Federer, Djokovic hit just six unforced errors and won 86% of points on his serve.
Further errors from Cilic saw Zverev race to a 5-1 lead before a classy backhand victor and a unreturnable serve sealed the second-set tiebreak, as well as the opening win.
Zverev is emerging as one of the Tour's brightest young stars after climbing to fifth in the world.
Djokovic was in action later on Friday against Croatian Marin Cilic but Zverev's win made that tussle academic, apart from the 200 ranking points and $200,000 on offer for each round-robin win at the event. Djokovic saved it with a service victor but then double-faulted to give the 21-year-old another opportunity.
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Having missed his chance, Zverev in the next game on a set-bol made a double fault, and in the second set and only won one game in two breaks of Djokovic.
Zverev was able to keep Djokovic at bay with his thunderous serve at the start of the first set.
Isner double-faulted to hand Cilic a decisive break in the eighth game of the second set and then did the same to gift Cilic a break at the start of the third. 'I would say about nine, nine-and-a-half (out of 10).
Djokovic had to wait a few hours to learn of his progress to the last four, which was confirmed thanks to a gritty fightback from former Wimbledon finalist Cilic.
Zverev had clearly read up on the scenarios to reach the semi-finals and waved his arms aloft in the air, knowing that even if he went on to lose Marin Cilic would need to beat world No. 1 Djokovic for the German to be eliminated. "John is such a tough opponent, the first set was unbelievably tight so I'm just happy to be through".
Djokovic said: "It's great to be back in the 02, it's been a lucky place for me over the years". With the markets pretty adept at pricing up matches featuring two high profile players, we've been forced to pick our spots this week, but I'd much rather that approach when the situation dictates.
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