Cilic entered the match with a dismal record at the O2 Arena - having won only one of his previous nine matches across three appearances at the tournament - but started strongly to break Zverev in only the second game of the opening set.
Djokovic appeared to be suffering with a cold and grabbed a tissue from his pocket on occasions, but after some fierce resistance in the opening set, he ran away with the match.
Djokovic, who helped Serbia win the title in 2010, is not convinced the two new events can survive. "But I managed to gather the strength when I needed it". Our tennis columnist, Dan Weston, previews the two matches.
Zverev gave Djokovic a set point with a spate of errors in the next game, and conceded it with a double-fault.
But this time the German went just wide with an attempted lob after the Serb ventured into the net.
Zverev was never the same after that.More news: Rams WR Kupp leaves Seahawks game with knee injury
"I thought I played well from mid-way through the second set. I expect him to play better than he did in Shanghai".
It was a crucial escape for the 14-time Grand Slam champion, who stepped up the pressure on Zverev to steal a hard-fought first set.
Djokovic, who replaced the injured Rafael Nadal at the top of the rankings last week, has stormed up the charts this year following elbow surgery and a period of indifferent form, winning Wimbledon and the US Open along the way.
Djokovic, who beat Isner in his opening group-stage match, has enjoyed a remarkable renaissance in the second half of 2018 and lifting the trophy on the banks of the River Thames would be the flawless way to finish his year.
Several leading players, including Djokovic, have questioned the timing of the ITF's flagship event, coming at the end of a gruelling 11-month season and Germany's Alexander Zverev said this week he would not play in the showpiece finals. If I break him at 4-all, we'll see where the match goes. Not just an Isner win will carry the Serb to the semi-finals but a Cilic win in three sets would do the same.
Breaks of serve were exchanged in the second set before Cilic was required to save a match point at 4-5.
Cilic wobbled briefly, handing the break back with a woeful game, but struck again with some bludgeoning groundstrokes and kept his composure to claim the win.