Federer earned a break in the third game of the second set, finishing with a stunning forehand, and it took until his fourth service game before he dropped a point on serve, as he began to peak.
Federer - and those supposedly sweaty palms of his - won 7-6 (3), 6-4, 6-4, showing why he is seen as the master of time as well as tennis ahead of turning 36 next month.
That came as a surprise admission from an 18-time grand slam champion aiming to win a record eighth title at the All England Club.
Zverev, into the Wimbledon third round for just the second time and first since 2008, is unfazed by his 0-4 record against Federer, saying he could accept defeat to one of the all-time greats.
"I think it's important to get through the first week with a good feeling", Federer said. 'The first one with the walkover didn't give me that much information.
Standing between Federer and his 14th Wimbledon quarterfinal in the last 15 years is buddy and bandmate Grigor Dimitrov.
Federer said he was unsure what to expect from Zverev, who has taken different approaches in their two meetings in 2017. "I'm very happy on my end". He was unable to do so again here, though the 29-year-old's serve-and-volley tennis is tidy.
GETTY Roger Federer certainly had plenty of support in Centre Court
The Swiss admitted he'd struggled with nerves in the opening set of his second round tie against Dusan Lajovic and there were again uncomfortable moments against the German but the world No. 5 always looked in control as he booked a match-up with Bulgaria's Grigor Dimitrov.
'He had a great run in the Australian Open.
There was a bit of an exhibition feel about Federer in the final stages before he clinched victory with his 13th ace.
For Mischa, as with the vast majority of Federer's opponents, the best tactic is to hope that the Swiss has an off-day. "He is at the ideal age right now to really understand his game, he is physically very strong, and I think mentally he has really taken that next step".
"It's a totally different ball game what she's going through than what I did". But yes, I think I can see maybe some of the plays that he does more than how he's hitting the shot or something like that.
However, even Roger Federer can't give birth although that hasn't stopped him thinking about what it might feel like if he could.