The 20-year-old Wozniacki was born more than a year after Date-Krumm made her Roland Garros debut in 1989. Date-Krumm made the French Open semifinals in 1995, retired the next season, then returned to the tour 12 years later.
Wozniacki made only nine unforced errors Monday, 19 fewer than her opponent.
The Dane had her left leg treated during her victory in the final of a clay-court tournament in Brussels on Saturday. She leads the tour with four titles in 2011.
Wozniacki is bidding for her first Grand Slam championship. She next faces qualifier Aleksandra Wozniak of Canada.