Häcken's Monica Jusu scored the only goal of the match when she chipped over Rosengård's Eartha Budd and made it 1-0 for the away team.
Rosengård had opportunities to equalize, especially in set pieces, but Jennifer Falk in Häcken's goal kept a clean sheet for the second time this season.
The loss comes after Rosengård wished to move the match from Saturday to Sunday. This because the team participated in a new seven-a-side tournament in World Sevens earlier in the week.
The Swedish Football Association denied the request.
Rosengård's participation in World Sevens has been criticized for being unprofessional.
When we got the question, it was a great opportunity for FC Rosengård and Swedish women's football to show themselves against the best teams in the world. We went down with good conditions, and we have worked down there (in Portugal) before this match against Häcken too, says Rosengård's sports manager Emelie Lundberg to Viaplay.
Häcken is now one point behind Hammarby, who tops the table, after the newly crowned cup winners' 0-2 loss to Kristianstad away.
Kristianstad took the lead early in the second half via Amy Sayer, and extended with five minutes left of the match through Katla Tryggvadóttir.
