He'll be eager to reach the quarter-finals for the first time, where he could come up against defending champion Roger Federer.
Williams has dropped the opening set in both her matches so far and needed to save match points to beat Bertens in Miami this year.
"I have played the qualies and three matches this week which were all three sets", said 29-year-old Rodina, one of six mothers in the draw at the start of the tournament.
Once the Czech survived a second-set tiebreak, she raced through the decider to make it through to the second week for the first time in seven attempts.
Struggling to stay in the set after half an hour, Williams found her huge serve just in time to hang on for 4-5.
The 32-year-old has made it to quarterfinals just twice in his career, including an appearance in last year's US Open final, where he lost to Rafael Nadal.
The defeat of the U.S. Open runner-up meant she became the seventh casualty in the top 10 women's seeds before the middle weekend.
The only past Wimbledon champion remaining in the field?
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Serena took her Wimbledon winning streak to 17 matches, thanks in part to 13 aces.
The American 25th seed moved into the second week without dropping a set and will next face Russian qualifier Evgeniya Rodina.
"Serena is my idol", Rodina said.
French Open semi-finalist Keys struggled for most of the match as she committed 48 unforced errors in a disappointing display.
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 American fought back from a set and two breaks down only to falter near the end.
Keys began play on Court 3 with goal and raced into a 5-2 lead in the opening set. But Keys won the next five games and broke again to level the set score.
"I worked really, really hard (to get back playing) and it's been a long, arduous road but I always expected to come out and do the best I can do". "I am a little surprised that I won, I was a little bit lucky today".