Linda Lif Boama opened the scoring in the 25th minute, and the score stood at 1-0 at halftime.
But in the second half, Kristianstad pulled away. In the 53rd minute, Tilda Persson made it 2-0, and 20 minutes later, Elin Hansson added a header.
Michelle de Jongh was substituted in the 63rd minute, and 24 minutes later she had scored twice after making it 4-0 and 5-0.
Norrköping is two points ahead of Rosengård in the relegation zone, and two points behind Djurgården in eleventh place. Kristianstad is sixth.
