The Elfsborg swimmer was the first of the Swedes to finish and set a personal record by three hundredths of a second, 54.43.
This advanced her to Monday night's semi-final in 12th place.
"To get "slammed" on the attempts when you've never felt satisfied. I've felt so damn bad from time to time," she says.
When the advance was secured, the tears came and she received a huge hug from the national team's press manager, Anna Hammar, in the mixed zone where the athletes meet the press.
The feeling afterwards?
"Both, it felt really good in the heat and I was really pumped and I know I can do well. But also that I just want to get out of here," says the 22-year-old.
Her reaction when she saw her time after a strong second-place finish:
"It feels great to do it in the first race. It feels like I've won everything," she says.
Dutchwoman Marrit Steenbergen, who broke Sarah Sjöström's world record over the distance in June, was fastest with 52.62.
Sjöström swims the 50-meter butterfly and 50-meter freestyle in Paris.
Åstedt will thus be the only Swedish swimmer in Monday evening's final session.
