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 Garcia, who she also beat at the French Open.
Williams, 31, chasing a sixth Wimbledon title and 17th major, wrapped up victory in 67 minutes with 30 winners and nine aces.
Date-Krumm reached the third round, 17 years after her last appearance, with a 6-4, 7-5 win over Romania's Alexandra Cadantu, 19 years the Japanese's junior.
Despite their many years on tour, Williams and Date-Krumm have never played each other on the tour.
"Kimiko is so incredibly fit and inspiring. I have never played her but I watched her when I was super-young," said Williams after winning her 599th career match.
"Venus has played her, so I will definitely be talking to her about it."
Wimbledon 2013: Serena Wiliams into third round
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