The world No. 2 was back in competitive action in London Sunday after taking it relatively easy over the last fortnight, and he served his way to a first-match 6-4, 7-6 (4) victory against Jack Sock at the O2 Arena.
"I'm happy that I was able to come out today and had actually good energy," said Federer, who broke Sock in the first game and won a remarkable 90 percent of points when he made his first serve. "This is the best I've felt since the Del Potro finals.
"I'm very happy to see that I didn't have to pay the price for taking it easy, you know, resting, recovering. But then turning it up the last few days got me in shape for today.
"Now I think I'm in the tournament. Now there's no more turning back. Just full steam ahead every match that comes."
In the night match, Zverev showed why just about everyone on the men's tour is predicting a dazzling future for him. In beating Cilic 6-4, 3-6, 6-4, the 20-year-old German produced a bit of everything, good and bad, and his fans will need strong nerves to stay with him as he establishes himself among the game's super elite.
On the positive side, there were great winners, backhand and forehand, a solid serve, and immense fighting quality. The negatives were an impetuosity in shot selection and occasional lack of tactical awareness that brought too many unforced errors -- and a temperament that boiled over a little too easily.
Cilic provided a stern test, even taking a 3-1 lead in the deciding set, but it was the younger player who showed the greater resilience in a match that lasted longer than two hours.
The next examination promises to be even more interesting, as Zverev faces Federer on Tuesday in another round-robin match in the Boris Becker group.
Zverev is one of only four players to have beaten the Swiss this year, although Federer's back was troubling him at the time, in Montreal last August.
"I played him a few times this year now," Zverev said. "I played him three times, if you count the Hopman Cup match we played. Obviously, all of them were great matches. Hopefully it can be another one."
Sock, 25, who will also face those two, had promised to "swing big" after sneaking into the year-end showpiece in the last Masters event of the year, in Paris, and he worked hard as well as taking risks.
His serve accuracy let him down a little but he found time to smile; he virtually asked Federer to hit a body shot when he was stranded at the net in the first set, and hit a tweener volley in the second set that deserved to win a point but didn't.
It was an engaging contest but Federer's clinical play was too much in the end. "Roger puts a pressure on you that I feel no other player really does," said Sock.
"I'll definitely be able to maybe hit my way into the next few matches, have some longer rallies, not feel the presence he puts on you when you're out there."