Top seed and defending champion Roger Federer needed just over an hour and a half to book a fourth-round spot by beating big-serving German Jan-Lennard Struff 6-3 7-5 6-2.
The 36-year-old Swiss extended his winning streak to 29 consecutive sets at the All England Club.
"I think I can be very happy today," said Federer, who will next face France's Adrian Mannarino.
"It's a wonderful feeling walking out there, I try to put on a good match and try hard every time, regardless of how many times I've played at Wimbledon. It's the most special court for me, hundreds of thousands must have come to see me play here."
Alexander Zverev considered not returning to his second-round match against Taylor Fritz on Friday but set sickness aside to power through.
Bad light on Wimbledon's Court One caused play to be suspended late on Thursday, with fourth seed Zverev struggling and trailing the world number 68 by two sets to one.
Darkness descended at just the right time as the German came back to win 6-4 5-7 6-7 (0/7) 6-1 6-2, though he thought about withdrawing due to an illness.
"Yesterday I had pain during the whole three sets," said Zverev, whose last five matches at a grand slam have gone to five sets.
"After the second set I actually went to throw up during the toilet break, then I felt a little bit better. But I felt very low on energy.
"Today in the warm-up I was actually maybe thinking about it, not to play at all.
"I was very low on energy, I didn't eat anything since yesterday.
"But then I thought, 'Well, if I don't feel well, it's going to be one set. If I feel better, it might be two.' I thought I'd go out there and try."
Gael Monfils made it through to the fourth round for the first time after beating Sam Querrey.
The mercurial Frenchman beat last year's semi-finalist 5-7 6-4 6-4 6-2 on Centre Court.
Monfils will tackle Kevin Anderson in the next round, and he enjoys a 5-0 winning record over the South African.
Anderson earlier became the first man through to the fourth round after beating Philipp Kohlschreiber 6-3 7-5 7-5.