In the earlier match, Zverev beat Cilic -- the Croat's 9th loss in 10-round robin matches in the Finals
The last time Novak Djokovic played at the O2 Arena he suffered a chastening defeat at the hands of home hero Andy Murray which confirmed the end of his dominance at the top of the men's game.
His return to the ATP Finals on Monday, after missing the 2017 edition because of an elbow injury, offered conclusive proof that the Serb is once again top dog.
The elastic-limbed 31-year-old, bidding to equal Roger Federer's record of six titles at the ATP's blue-riband event, produced an immaculate display to tame American giant John Isner, who was making his tournament debut, 6-4, 6-3.
Already guaranteed to end the year as world number one after winning Wimbledon and the US Open, Djokovic is a massive favourite to complete an incredible resurgence from world number 22 in June with another title in London's docklands.
He will now set his sights on Germany's Alexander Zverev in his second round-robin match after the exciting 21-year-old beat Croatia's Marin Cilic 7-6 (5), 7-6 (1) to open his account in the Gustavo Kuerten group earlier in the day.
Isner, at 33 the oldest first timer at the eight-man season-ender since Andres Gimeno made his debut aged 35 in 1972, was not overawed but never managed to lay a glove on Djokovic in the 73-minute contest.
Djokovic lost only four points on his own serve in the first set but what was most worrying for Isner was the way his opponent managed to read his towering delivery, pinging back returns to the baseline with monotonous regularity.
"He's the best returner I've ever faced for sure," Isner said. "Sometimes you got to hope he's a bit off. Unfortunately, I don't think that was the case tonight. I got my ass kicked."
Having failed to convert break points in Isner's opening two service games, Djokovic made no mistake when another chance came along, belting a forehand return for a winner and a 4-2 lead.
Isner saved a set point when serving at 3-5 and banged down three consecutive aces to stay in the set but Djokovic calmly held to seize the opener.
The writing was on the wall for Isner when Djokovic broke serve at 3-3 in the second set -- the Serb roaring his approval. Two games later Djokovic sealed victory with a crosscourt backhand winner.
While the O2 Arena has been a happy hunting ground for Djokovic with four of his five ATP Finals titles arriving there, the same cannot be said of four-time qualifier Cilic.
The Croat's defeat by Zverev -- a repeat of his loss to the German 12 months ago -- means he is 1-9 for the tournament.
Cilic would have been kicking himself after allowing a first set that he initially dominated slip from his grasp.
He had points for a 4-0 and 5-1 lead but allowed world number five Zverev to hit back and win the opening set on a tiebreaker, sealing it with a sublime backhand pass.
Breaks of serve were exchanged in the second set before Cilic was required to save a match point at 4-5.
A second tiebreak arrived and just as in the day's first shootout, it was Zverev who jumped into a lead against an edgy Cilic who double-faulted at 1-4.
Zverev nailed a backhand winner down the line to earn five more match points and converted the first with a powerful first serve that Cilic fenced into the net.
"I was just trying to get myself going, trying to get the energy up. It worked out," Zverev, who vented his anger in the direction of coach Ivan Lendl in the early stages, said.
His task now will be to avoid last year's let-down when, after beating Cilic on his debut match, he then lost to Roger Federer and Jack Sock to miss out on the semi-finals.