Earlier, Zverev saw John Isner 7-6 (7/5), 6-3 to get to the semifinals of the finals for the first time, which means that Djokovic-Federer's finale remains an opportunity.
Djokovic, dressed in black, won exceptionally 31 points in the row from the third match of the first set to the fourth match of the second against the determined Chilean, who could not progress even with a win.
"Obviously I knew before the game I was already qualified and I knew who I was playing, so it's not easy to access this match with 100% readiness to win," Djokovic said.
"But this is a unique format and we both wanted to win from the first point. It was the first set that probably decided to match.
"(Anderson) plays excellent tennis, it's definitely his best season and he continues this during the tournament. He plays well, he is well served, very aggressive, so I know what to expect."
In a high-quality competition, the 14-year-old Grand Slam champion remained calm to keep the set point in the first set during the break before he took 9-7 on his second set.
In the second set, Djokovic immediately submitted the service to Cilic under a lot of pressure.
The Croatian former US American champion opened deep to stay in the competition in the early stages, but he broke up in the fifth match, giving himself a climbing climb, and also succumbed to the next service game, leaving Djokovic to serve as a winner.
Djokovic, who has not dropped a set in three races in London, enjoys a remarkable renaissance in the second half of the season following an elbow and an indifferent form earlier in the year.
He lost only two games since early July, winning Wimbledon and the US Open on the road, and appeared once again as the man who defeated when he tried to retire with Federer in six ATP Finals titles.
Zverev was aware that the victory of any result against the American giant Isner would be taken in the semifinals.
The turning point came at the end of the 12th game, when the 21-year-old German saved a set of points at his service with a time that went to the competition he won.
In the second set, the only pause in the eighth game became decisive and Zverev served for victory.
"It's obviously great to get to the semifinals," he said. "But the tournament is not over, I'm in semifinals, there are only good opponents, there is only the best in the world.
"Tomorrow I will play Roger, which will be very difficult, but I hope this will be a great match. We will see how far I can go."
Third seed Zvereva, coach Ivan Lendl, is the youngest semifinals at the ATP finals of Juan Martín del Potro in 2009.
The other Federer, who propelled his 100th title, beat Anderson in the right set on Thursday in the quarter-finals of the Lleiton Hevitt Group, but both players progressed, meaning early exits for Kei Nishikori and Dominic Thiem.