Struff, who had recovered from 2-0 down to win both of his opening two matches, settled down in the second set and was clearly becoming more comfortable in the alien and daunting environment of Centre.
The 36-year-old Swiss has won 26 consecutive sets at the All England Club. "I am a little surprised that I won, I was a little bit lucky today".
Federer is having no such problems and eased past Jan-Lennard Struff 6-3 7-5 6-2.
Federer next faces French 22nd seed Adrian Mannarino.
The world number 64 has had to fight back from two sets to love down in his first two matches to beat Leonardo Mayer and 39-year-old Ivo Karlovic. He also made it to the Australian Open quarterfinals in 2016.
Zverev had trailed two sets to one when his tie with Fritz was halted due to darkness on Thursday.
But the 21-year-old raced away with the last two sets in Friday's bright sunshine.
"I'm happy I found a way today".
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Keys added: "It's definitely been a challenge that I have had to deal with where all of a sudden I'm the one that's supposed to win and people are playing with nothing to lose and playing their best tennis".
This is Williams' fourth tournament since giving birth last September to Alexis, her first child with husband Alexis Ohanian.
The seven-time champion came from a break down in the first set to get past Kristina Mladenovic 7-5, 7-6 (2).
Of the players seeded in the top 10 ahead of the tournament, only world number one Simona Halep, seventh seed Karolina Pliskova and five-time Wimbledon champion Venus Williams, seeded ninth, are left in the draw after just five days.
However, the dominant way he played in his 6-3 7-5 7-5 victory over German Philipp Kohlschreiber suggested he could go further than ever before.
The South African eighth seed reached the third round when he completed a four-set victory over Italy's Andreas Seppi on Thursday.