Top seed Williams extended her winning streak to 33 matches, just two behind the record set by sister Venus in 2000, with a 6-3, 6-2 win over French 19-year-old Caroline Garcia, who she also beat at the French Open.
Williams, 31, chasing a sixth Wimbledon title and 17th Major, wrapped up victory, the 599th of her career, in 67 minutes with 30 winners and nine aces.
Date-Krumm, 42, reached the Wimbledon third round, 17 years after she last did so, with a 6-4, 7-5 win over Romania's Alexandra Cadantu, 19 years the Japanese's junior, to become the oldest woman to make the last 32 at the All England Club.
Despite their many years on tour, Williams and Date-Krumm have never played each other.
"Kimiko is so incredibly fit and inspiring. I have never played her but I watched her when I was super-young," said Williams.
"Venus has played her, so I will definitely be talking to her about it."
Date-Krumm made the semi-finals in 1996 where she lost to Steffi Graf before taking what turned out to be a 12-year break from tennis.
After the shockwaves of Wednesday, which saw Roger Federer and Maria Sharapova knocked out and world number two Victoria Azarenka one of a record seven injury withdrawals and retirements, normal service was resumed Thursday.
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