In the women's draw, seven-times victor Serena Williams overcame her first big test in confident fashion by beating France's Kristina Mladenovic 7-5 7-6 (2).
But Djokovic snapped out of his torpor and took charge once he broke in a marathon seventh game of the second set. We played in dark for an hour. I mean, he doesn't give his opponents anything.
"I actually started off well".
The 19-year-old will faces U.S. ninth seed John Isner for a place in the quarter-finals.
He will next face Ernests Gulbis.
"This is only my second serious tournament back", said Williams, who is returning from a maternity leave.
Stefanos Tsitsipas became the first Greek man in the Open era to make the last 16 of a Slam as the 31st seed beat Italian qualifier Thomas Fabbiano 6-2, 6-1, 6-4.
'I think that he's a future Grand Slam victor. The Czech faces Dutch 20th seed Kiki Bertens, who stunned five-time Wimbledon victor Venus in the third round.
No one has managed more wins on the ATP Tour this year than Zverev.
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The 36-year-old Serena faces Russian qualifier - and fellow mother - Evgeniya Rodina in the last 16.
He staged another impressive escape act on Court One, winning the final two sets to move into the third round. "Thought I'd go out there and try". "I feel 100 percent comfortable with contacts".
"Today in the warm-up I was actually maybe thinking about it, not to play at all".
Frenchman Gael Monfils reached the fourth round at Wimbledon for the first time in 10 appearances, beating last year's semi-finalist Sam Querrey 5-7 6-4 6-4 6-2.
"I'm very calm. I try to find ways to win".
However, he has only once made the last eight of a slam once - at this year's French Open - and the fourth seed suffered the indignity of being bagelled in the final set on Court No.1 as world number 138 Gulbis triumphed 7-6 (7-2) 4-6 5-7 6-3 6-0.
"Stopping at 2-1 down was not a nice feeling but I played better than yesterday", said Zverev. But I always say the same: "Roger and Rafa Nadal are the favourites, although there are many players who can be important in the last matches too".
The fourth seed had a tougher time against Fritz than eighth seed Kevin Anderson did against Philipp Kohlschreiber, with the German served into straight-sets submission 6-3, 7-5, 7-5.
Despite being widely-tipped to be a Grand Slam threat, it was another letdown for Zverev whose run to the quarter-finals at Roland Garros last month remains his best performance at the majors.