But it was easier going thereafter for Federer as he won the second and third sets in comfortable fashion to close out the match inside two hours.
While the 18-time Grand Slam champion had never even dropped a set to the German in the past, his serve-and-volley style can be unpredictable at the best of times and the Swiss maestro was constantly forced to improvise.
There were baseline battles too, often settled by Federer's stylish one-handed backhand. "It is important to get through the first week with a good feeling", he said after his win.
Standing between Federer and his 14th Wimbledon quarterfinal in the last 15 years is buddy and bandmate Grigor Dimitrov. I'm very happy anyway.
The umpire took a sharp catch when Federer mistimed a return right at him and by coincidence was hit by Zverev one game later, although he was not fast enough to take the catch on the second occasion.
Zverev had faced Federer four times, failing to win a set in any of those losses.
The 13th-seeded Bulgarian built a 6-1, 6-1 lead over Dudi Sela when the 32-year-old Israeli, drained from winning successive five-set fights over Marcel Granollers and John Isner, pulled the plug. "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".
From the second set on, Federer was in complete control. We could have nearly played in the Australian Open final against each other.
That's not to say he didn't endure nervy moments, though, with the Swiss throwing away a 4-1 lead in the opening set to allow his opponent to force a tiebreak.
There was a bit of an exhibition feel about Federer in the final stages before he clinched victory with his 13th ace.
"It's a totally different ball game what she's going through than what I did". I will try to go all or nothing, maybe even more than before. I think I'm doing the things the right way in order for me to put myself into those kind of positions, in terms of to hopefully win a Slam one day. "Today I feel 50 per cent better than I did two days ago".