With rain delaying the start of play by two hours and more scheduled for throughout the day, the 2010 finalist in Paris was clearly in no mood to waste time as she rattled off the first nine games before allowing her 42-year-old opponent to get on the scoreboard.
Stosur, who converted five of eight break points while not facing one on her own serve, will face Kristina Mladenovic of France in the second round.
Date-Krumm, who made her French Open debut 24 years ago in 1989 when 57 women in this year's singles draw were not even born, lasted only 64 minutes on Court One.
"I guess, lucky for me I was able to finish the match before this last downpour came," Stosur, runner-up in 2010, said. "It was spitting a little bit when we went out there. You think, oh, are we going to start, or are we not?"
Date-Krumm, who reached the semi-finals of the French Open in 1995, but also played in the last four of Wimbledon (1996), and the Australian Open (94), reached a career No.4 in the WTA rankings that year but it did not exactly fulfil her.
"Sometimes I was crying on the airplane because I didn't want to stay out of Japan," Date-Krumm, the third oldest woman to play singles at Roland Garros, said.
Date-Krumm quit at the end of 1996 but, after a 12-year hiatus in which she met her husband, German racing car driver Michael Krumm, she returned to the sport.
"After I stopped tennis, I enjoyed a normal life. Then I married with a German guy and I changed a lot," she explained.
Date-Krumm admits her preparation for Roland Garros was not ideal, playing not one match on clay this year, and she was duly thrashed by former runner-up Stosur.
"I didn't play on red clay even once this year, because for many years, when I played in the red clay tournaments, I would lose in the first round, first round, first round, and then I would get injured," she said.
"I've got doubles here then I'm already focussed on the grasscourt season."
9-Samantha Stosur (Australia) beat Kimiko Date-Krumm (Japan) 6-0 6-2
13-Marion Bartoli (France) beat Olga Govortsova (Belarus) 7-6(8) 4-6 7-5
16-Dominika Cibulkova (Slovakia) beat Lesia Tsurenko (Ukraine) 6-1 6-4
18-Jelena Jankovic (Serbia) beat Daniela Hantuchova (Slovakia) 6-4 7-6(7)
27-Yaroslava Shvedova (Kazakhstan) beat Coco Vandeweghe (U.S.) 6-0 3-6 6-2
31-Alize Cornet (France) beat Maria Joao Koehler (Portugal) 7-5 6-2
Mariana Duque (Colombia) beat Kristyna Pliskova (Czech Republic) 6-2 6-0
Kristina Mladenovic (France) beat Lauren Davis (U.S.) 6-0 7-5
Silvia Soler Espinosa (Spain) beat Irina Begu (Romania) 6-3 6-2
Marina Erakovic (New Zealand) beat Elena Baltacha (Britain) 6-3 6-0