The German - runner-up to Serena Williams at the All England Club past year - needs to reach the final again to retain her place at the top of the rankings but was given a real scare by her American opponent.
The top-ranked Kerber has lost her past four matches against Muguruza.
However, the 29-year-old showed her pedigree to hold and win the next two games, bringing the set back on serve. "I thought I raised the level of tennis", said Djokovic after making the second week without dropping a set.
Kerber and Muguruza have met on seven occasions but it is the Spaniard who edges the head-to-head record, having won each of the last four encounters, including one at Wimbledon in 2015.
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People protest against the gathering of European leaders on the upcoming G-20 summit in Hamburg, Germany, Sunday, July 2, 2017. The informal meeting will be attended by the BRICS leaders, who will hold their summit in September in Xiamen, south China.
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A five-time Wimbledon champion, Williams , seeded No. 10, had just defeated Elise Mertens , 7-6 (7), 6-4, in 1 hour, 40 minutes. The reporters gave Williams about a minute to collect herself, before she chose to end the press conference early.
"I definitely will take some confidence from this win today" Rogers said.
Milos Raonic, last year's runner-up at Wimbledon, advanced to the tournament's second week by beating 25th-seeded Albert Ramos-Vinolas of Spain 7-6 (3), 6-4, 7-5 with the help of 21 aces, including one to end it.
Kerber was a break down in the second set but did just enough to claw her way into the fourth round where she will face Garbine Muguruza, after World No. 15 raced into the fourth round with a 6-2, 6-2 victory over Sorana Cirstea. "Comparing to the first couple of matches and the last couple of weeks I think this was the most focused I was on the court".
The deft Radwanska, the 2012 runner-up to Serena Williams, came back from a set down to beat 19th seed Timea Bacsinszky 3-6, 6-4, 6-1, and now faces eighth seed Kuznetsova who cruised through 6-4, 6-0 over qualifier Polona Hercog. However, Leander Paes and Yifan Xu, and Zhaoxuan Yang and Divij Sharan lost their first-round matches late on Friday. "Every time I start the grass season, I'm like, 'How the hell did I reach that final?'", the 2016 French Open victor said. "I expected a lot of tricky shots from her and a lot of entertaining rallies", said the Polish ninth seed. Kerber won her first two major titles at the Australian Open and U.S. Open in 2016. Slovakian Magdalena Rybarikova, who knocked out third seed Karolina Pliskova in the second round, dispatched Lesia Tsurenko of Ukraine 6-2, 6-1 and Croatian Petra Martic beat Zarina Diyas of Kazakhstan 7-6 (6), 6-1.