Bodin opened the scoring in the 38th minute before Anna Anvegård added to the lead in first-half stoppage time.
Barely two minutes into the second half, Thelma Palmadottir made it 3-0, before Bodin struck again. After an own goal made it 5-0, Bodin completed her hat trick when she made it 6-0.
The 24-year-old striker joined Häcken from league rivals Växjö just a few days ago, and scored three goals in her first match for the club.
It's a debut you can only dream of, so it's great fun, Bodin told Viaplay.
Häcken leads the women's Swedish championship by five points ahead of Hammarby, who have one fewer game to play. BP is ninth.
