In the 22nd minute of the first leg against Chelsea, Blackstenius stepped up and headed in to make it 1-0. The 30-year-old later made way for Alessia Russo, who determined the final score.
It is the third consecutive match that Blackstenius has scored for Arsenal after the calf injury which kept her out for three matches.
The victory puts Arsenal in a good position for the second leg of the quarter-finals, which will be played on April 1.
Johanna Rytting Kaneryd came on for Chelsea in the 57th minute. Smilla Holmberg came on for Arsenal in the 78th.
