The 36-year-old American now can not meet a top 32 player until the semi-finals after the scattering of the seeds this week.
Former champions Novak Djokovic and Rafael Nadal remained on course for a semifinal meeting.
The 36-year-old is bidding for a ninth title at the All England Club and maintained his fine progress through the opening week with a 6-3 7-5 6-2 win despite the best efforts of his German opponent.
Serena Williams's chances of winning an eighth Wimbledon and 24th Grand Slam title were boosted Friday when Madison Keys became the seventh top 10 seed to be eliminated. She also won her 18th consecutive match on grass courts dating to 2015 - the second-longest streak of her career (20 from 2002 to 2004).
The 17-times Grand Slam champion dug in though and managed to avoid being dragged further into the afternoon, claiming victory when Kukushkin's forehand smacked into the net tape.
Keys lost in three sets behind a faltering serve, and gave up seven break points to Rodina. But he easily held serve in the next game and broke Zeballos again to close out the match.
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However, Southgate did warn that England should not get ahead of themselves as they still have to get past Colombia, who reached the last-eight of the 2014 World Cup.
In a match full of big swings, Keys led 5-2 in the first set before Rodina won the next nine games to go 4-0 up in the second. After the double fault in the first set, Mladenovic appeared to lose her confidence. "I am a little surprised that I won, I was a little bit lucky today".
Makarova, who made the quarter-finals four years ago, beat a weary-looking Lucie Safarova of the Czech Republic 4-6, 6-1, 6-4.
"Yesterday he was playing so, so good, and hitting the ball so hard that I couldn't do anything", the 82nd-ranked Pella said. "I feel ready to compete".
Nick Kyrgios, the 15th seed, also advanced in straight sets, beating Dutchman Robin Haase 6-3 6-4 7-5 to book a date with Kei Nishikori, who ousted Kyrgios's fellow Australian Bernard Tomic 2-6 6-3 7-6 (9-7) 7-5. The second set went back and forth, with both players getting advantages before finally it went to a tiebreak.
Having made 18 unforced errors in each of the first two sets, Giorgi tightened up her game to make just eight in the third and advance to the last 16 at Wimbledon for the first time since 2012.
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