Anderson had a chance to take an early lead against Djokovic, but he overhit a forehand on set point in the 12th game of the match.
"I did everything I meant to do on my end, " Djokovic said.
Zverev will next play second-seeded Djokovic in the semifinals.
Friday's four favourites triumphed - an outcome which was around a [3.50] shot based on the prices available at the time of yesterday's preview, and I certainly don't see any reason to adapt my point of view that the matches were accurately priced by the market.
"I knew I had to step it up too, and I was able to do it, so it's a good feeling to have, no doubt about it".
Celebrating his 1,000th match in style, the 14-time Grand Slam victor Djokovic was clinical against a shell-shocked Zverev. "I wasn't, I feel like, playing as well as I'm playing today".
Djokovic surprisingly let three match points go begging at 5-1 40-0, but took his fourth chance to wrap up the most emphatic of victories in exactly an hour.
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The top seed said he lacked "punch on the ball" but felt "explosive" on court, though he said he could have improved his serves.
The 21-year-old Zverev was off-colour most the match and bad tempered at times, angrily throwing his racquet at the start of the second set as Djokovic ramped up the pressure. "It's going to be definitely a close match".
The final will be played on Sunday in China.
The top four players in the world - Nadal, Federer, Djokovic and Juan Martin del Potro - had already qualified for London.
The third-ranked Djokovic taught Zverev a lesson.
Zverev, now under the tutelage of Ivan Lendl, said he is pleased with his overall progress, even if a maiden Grand Slam remains elusive.
Novak to me right now looks like the best player on the planet and looks like the guy who is dominating men's tennis. I love the way I have played so far this week.
'You are always trying to stay centered and balanced.
"Against that kind of player, you need something to hold on to, " he said.