Linköping has had a fine season so far and took advantage of Rosengård's loss against Piteå on Friday.
With the team's safe 4-0 victory against BP, they climbed past and up to the top of the table.
Therese Simonsson broke the deadlock after barely an hour of play and within 20 minutes Linköping had scored four goals, through four different goal scorers.
The 3-0 goal came from Danish shooting league leader Amalie Vangsgaard – her 14th goal of the season.
The top battle in the women's league is a real thriller with three teams within two points.
Linköping has 40 and Rosengård and Kristianstad have 39. However, the Malmö team has played one game less.