Things had a familiar feel early on as Federer raced into a 4-1 lead but Zverev began to rush the seven-time champion and the German fought back to level.
Federer wasted no time in asserting his dominance over Zverev, perhaps eager to avoid the relatively slow start he had made in his previous match, against Dušan Lajović.
"I was just there supporting my wife", said Federer, father to two sets of twins.
"I think it important to get through first week with good feeling", added Federer, who has only lost before the last-16 twice in his last 50 Grand Slam appearances. Mischa's a great guy and I think we fed off each other and played a good match.
These two have played five times and Federer has won all five meetings.
"I'm not that surprised because I thought that everybody this week was going to find their form, especially speaking about Andy and Novak".
Zverev had faced Federer four times, failing to win a set in any of those losses.
It was almost a double break two games later but Zverev rallied to hold and in what was his first Centre Court appearance, he will have been glad to make Federer serve it out. Without playing superb tennis or blowing his opponent away in the rallies, the 35-year-old controlled the pace and avoided trouble. "The first match was obviously cut short and didn't give me that much information about my game, but it did help me to save energy".
Federer was more than happy with his evening's work.
There were moments of levity, when Federer hit the umpire with a wayward return before Zverev did the exact same a game later, but otherwise it was all business on Centre. We could have nearly played in the Australian Open final against each other.
The Swiss had to take the first set via a tie-break with the 27th seed ensuring that his illustrious opponent was forced to battle to gain the ascendancy.
However, even Roger Federer can't give birth although that hasn't stopped him thinking about what it might feel like if he could. With me, I hoped I was going to be there. "He is at the flawless age right now to really understand his game, he is physically very strong, and I think mentally he has really taken that next step". I will try to go all or nothing, maybe even more than before.