The 20-year-old, who reached the end-of-season event at London's O2 Arena courtesy of a successful year in which he picked up Masters tournament victories in Montreal and Rome to sit third in the world rankings, looked comfortable as he took the first set thanks to a single break of serve.
But former US Open winner Cilic hit back in the second set as he won the opening three games on his way to levelling the match.
Zverez was in trouble in the deciding set when Cilic again broke his serve, but this time he fought back and finally edged out the 29-year-old Croatian 6-4 3-6 6-4.
Afterwards, the German, who is the youngest World Tour Finals qualifier since Juan Martin del Potro in 2008, said: "For the most part of the second and third set he was the better player.
"I was just happy to come back and win. If you have the opportunity to play here you have to take it. We both played well today, but I'm happy to get the win.
"It is different walking on here than any other stadium. The crowd, the atmosphere is amazing.
"There were a lot of nerves involved in my first match. Obviously I'm happy that's behind me. I'm happy that I won."