In the second game, Isner made a comeback to hold through 3-3, however, the American overplayed a low forehand approach shot which gave the second break to Djokovic to ultimately win the game.
There were few moments to test the 02 Arena's crowd decibel-level monitor - a new gimmick this year - but despite not feeling well, Djokovic had too much guile for Zverev.
The victory over fourth-seed Anderson in the Lleyton Hewitt Group takes Federer through to the semi-finals for the 15th time in 16 attempts at the season-ending finale and means he will likely avoid a meeting in the last four against in-form Novak Djokovic.
A tired looking Cilic saved a match point to take it to another breaker, but his forehand continued to misfire and he again opted against challenging when his second serve was wrongly called out as Zverev wrapped up his 55th win of the season.
Djokovic showed just why he has been installed as favourite for the tournament in London as he produced a masterclass to clinch victory over Isner with Ronaldo courtside. "It wasn't a great quality tennis match, to be honest".
This time Zverev traded blows from the baseline before drawing Djokovic to the net, but he just missed the target with a topspin lob that landed in the tramlines.
The last two matches for him against (Marin) Cilic and me could have gone either way. Zverev, who arrived in London having won three titles in 2018, had early chances to break at 1-0 and 3-2 but it was Cilic who edged in front after a weak backhand from the German handed his opponent the break.
Speaking about his chances of winning a 6 ATP World Tour Finals and the group scenario ahead of Wednesday's game, Djokovic said, "I'm feeling fit physically and mentally".
Zverev has booked his place in the semi-finals after overcoming John Isner on Friday, who he beat 7-6, 6-3. He's a major player in the sport, and promises to be for years to come.
"Tactics were superb. He served better, improved dramatically from his second match again".
The German should have put away a backhand for three break points in a fifth game which Cilic won and gestured to his box after the fifth seed moved a game away from taking the opening set. "It takes a little bit of time really to get yourself adjusted to the surface because the surface is a good surface".