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."
Results from the fourth day of Wimbledon (x denotes seeded player):
Men's singles:
Second round:
Feliciano Lopez (ESP) bt Paul-Henri Mathieu (FRA) 6-3, 5-1 - retired
Richard Gasquet (FRA x9) bt Go Soeda (JPN) 6-0, 6-3, 6-7 (5/7), 6-3
Bernard Tomic (AUS) bt James Blake (USA) 6-3, 6-4, 7-5
Kevin Anderson (RSA x27) bt Michal Przysiezny (POL) 6-4, 7-6 (7/2), 6-4
Tomas Berdych (CZE x7) bt Daniel Brands (GER) 7-6 (8/6), 6-4, 6-2
Igor Sijsling (NED) bt Milos Raonic (CAN x17) 7-5, 6-4, 7-6 (7/4)
Ivan Dodig (CRO) bt Denis Kudla (USA) 6-1, 7-6 (7/4), 7-5
Kei Nishikori (JPN x12) bt Leonardo Mayer (ARG) 7-6 (7/5), 6-4, 6-2
Andreas Seppi (ITA x23) bt Michael Llodra (FRA) 7-5 - retired
Juan Martn Del Potro (ARG x8) bt Jesse Levine (CAN) 6-2, 7-6 (9/7), 6-3
Women's singles:
Second round:
Serena Williams (USA x1) bt Caroline Garcia (FRA) 6-3, 6-2
Kimiko Date Krumm (JPN) bt Alexandra Cadantu (ROM) 6-4, 7-5
Sabine Lisicki (GER x23) bt Elena Vesnina (RUS) 6-3, 6-1
Samantha Stosur (AUS x14) bt Olga Puchkova (RUS) 6-2, 6-2
Marina Erakovic (NZL) bt Peng Shuai (CHN x24) 7-6 (8/6), 6-2
Madison Keys (USA) bt Mona Barthel (GER x30) 6-4, 6-2
Tsvetana Pironkova (BUL) bt Barbora Zahlavova Strycova (CZE) 7-5, 6-3
Petra Martic (CRO) bt Karolina Pliskova (CZE) 7-6 (9/7), 6-1
Roberta Vinci (ITA x11) bt Jana Cepelova (SVK) 6-1, 4-6, 9-7
Dominika Cibulkova (SVK x18) bt Maria Teresa Torro-Flor (ESP) 6-0, 6-1
Klara Zakopalova (CZE x32) bt Annika Beck (GER) 7-6 (7/5), 6-3
Li Na (CHN x6) bt Simona Halep (ROM) 6-2, 1-6, 6-0