Djurgården had the most dangerous chance of the first half when Victor Edvardsen got free after a brilliant counterattack, but could not get the ball past the goalkeeper.
However, Edvardsen got another chance just a minute later, this time from the penalty spot after Rondon Fernandez took the ball with his hand, and rolled the ball in via one post.
Five minutes later, Joel Asoro stayed in front and scored 2–0.
Asoro with solo performance
The 23-year-old, who was bought from Swansea last summer, was not done there.
In the 54th minute, Isac Hien gave him the ball just inside the attacking half.
Asoro jogged to the penalty area and thumped the ball in at the far post with his left foot.
Djurgården had a somewhat bitter end after Marcus Danielson picked up a penalty, but after 1-3, Djurgården have great chances to make the playoffs to the Conference League, which is the last round to get into the tournament's group stage.
The return is played in Stockholm next Thursday.