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.
Earlier, in the day, three-time champion Novak Djokovic silenced a raucous Centre Court crowd as he came back to beat home favourite Kyle Edmund 4-6 6-3 6-2 6-4 in the third round of Wimbledon.
Gulbis' win on Saturday was his third successive five-setter having also played three matches in qualifying.
The 21-year-old from Germany is ranked at No 3 in the world but has not yet won a Grand Slam.
"I think I can be very happy today", said Federer, who will next face France's Adrian Mannarino. The match today showed I can't take anything for granted.
Gulbis is now ranked 138th and he is the first qualifier in the last 16 at Wimbledon since Brian Baker in 2012.
Zverev said he was returning much harder on Friday, rushing Fritz and giving him less time to react. In a tough match, Williams overcame a slow start to show fight in a 7-5, 7-6 win. Things happen. I thought after I won the third set, I'm going to get out with a win.
"After the second set I actually went to throw up during the toilet break, then I felt a little bit better".
With everything on the line, de Minaur forced Nadal into longer rallies, giving one of the trademark performances that have distinguished him as a promising young player.
"That was my plan to do in the second set and in the third, and obviously it worked well".
"I think he's a future grand slam victor", Gulbis said.
Kontaveit won with a score of 6-2, 7-6 (4). "I realised that he was getting exhausted, yes, so".
Russian qualifier Evgeniya Rodina outplayed an erratic Madison Keys in a 7-5 5-7 6-4 victory to reach the fourth round of a Grand Slam for the first time in her career. Raonic, the No. 13 seed from Thornhill, Ont., led 6-5 in the third set when play resumed.
U.S. Open finalist Kevin Anderson struck an impressive 42 winners on his way to the fourth round, beating Germany's Philipp Kohlschreiber 6-3 7-5 7-5.