The two players had some history, with Date-Krumm winning their only previous meeting at Osaka in 2010 - that actually made Date-Krumm the first 40-something in WTA history to beat a Top 10 player.
This one was nothing like that, though, as the No.9-seeded Stosur won the first nine games and, after the two traded holds the next few games, broke one last time at love to seal a 60 62 victory.
"I was very pleased with the way I played and the way I started the match," Stosur said afterwards. "Then the start of that second set I really had to keep going and not allow her to really feel like she could get into it. I was very pleased how I did that. I thought my slice was good and I served well too."
It was a wet day in Paris - play didn't start until almost three hours later than scheduled, and there was drizzling throughout Stosur's match. How did the Australian cope with the late and damp start?
"Just sat in front of the coffee bar," Stosur said. "We got a good table. Just waited around, waited for the next update, had something else to eat. And as soon as it looked like I was going to go on, I went down to the locker room and did what I needed to do. I was happy to get out there and start."
Though Stosur's best Grand Slam result was her title run at the 2011 US Open, she has actually had her best overall results here, reaching the finals in 2010 and two semifinals in 2009 and 2012. But the Australian isn't looking further than her next match, let alone any deep rounds like those ones.
"The first hurdle is done, but there are many, many more ahead of me," she said. "I certainly don't get ahead of myself. I've played enough tournaments to know you can't look at the draw and pencil yourself into a final and think it's going to go the way you think it's going to go or you want it to go.
"One match at a time," she added. "I don't shy away from the draw - I don't say, 'Don't tell me.' You always find out eventually. But yeah, I'm certainly not looking ahead of the next match."
Despite the loss, Date-Krumm remains one of the most intriguing storylines around, a former World No.4 who came back after more than 11 years out and is still doing a lot of winning on the tour.
"I still have passion," Date-Krumm said. "When I was young in the '90s, I was not enjoying the tour. I always felt like I was not enjoying the tennis; I was not enjoying the tour; I was not enjoying anything. Sometimes I would cry on the airplane because I didn't want to leave Japan and be unhappy.
"When I stopped playing tennis, I enjoyed my normal life. I got married and I changed a lot. But I still loved tennis - I enjoy it now much more than before. I have so much passion right now."
Date-Krumm was playing her first clay court match of the year - well, technically, as she did play doubles last week in Strasbourg, and actually went all the way to the title with Chanelle Scheepers.
"I didn't play on red clay once this year, because for many years I played red clay tournaments but every time I lost first round, first round, first round, and then I got injured. So this year I changed my scheduling and didn't play singles. I only played doubles last week in Strasbourg. Before the red clay season I decided I wouldn't play. It's not my surface. Everybody knows it. And I know it too!
"I also didn't want to get injured before the grass season. So I'm disappointed to lose, but also happy I didn't get any injuries today. Anyway, now I'm just trying to focus on doubles here, and then I'm already focused on the grass court season that's coming up. So yeah, everything's okay now."