The Australian, who lost to Francesca Schiavone in the final in 2010, has an excellent recent record at Roland Garros having reached at least the semi-finals in three of the last four years.
On Tuesday, Stosur was up against the remarkable 42-year-old Kimiko Date-Krumm but it was not a good afternoon for the Japanese player, who failed to win a game until she was 6-0 3-0 down.
She then rallied but ninth seed Stosur was only held up briefly as she eased to a 6-0 6-2 victory in an hour and four minutes.
The rain, which had delayed the start of play for more than two and a half hours, then returned to Paris, with Stosur's one only of only four matches to be completed.
With so much time lost, matches scheduled later in the day began to be cancelled, including Heather Watson's.
The British number two, who is making her return after more than two months out with glandular fever, had been due to meet Swiss Stefanie Voegele in the fourth match on Court Three.
Stosur had been in poor form on clay prior to the tournament in Rome two weeks ago, but a run to the semi-finals, where she pushed Victoria Azarenka hard, has put the Australian in good spirits.
She said: "The tournament in Rome was good, and I feel like I have practised very well leading into today's match. I thought I played well today.
"The first hurdle is done but there are many, many more ahead of me. I have got to stay on track but I think this was a very good start."
Stosur was also happy to get her match over quickly, saying: "When I was playing, it was actually not too bad. It was spitting a little bit when we went out there. You think, 'Oh, are we going to start, are we not?'
"Luckily for me, I was able to finish the match before this last downpour came. So I guess it's the best way to deal with sometimes a frustrating situation."
The heavy downpour was reasonably brief, and the players returned to court just over an hour after leaving it.