Elfsborg had a nice result before the match on Sunday - a loss of eight matches.
AIK, on the other hand, had a scorching loss against Mjällby in the bag.
The Stockholm team started strongest, but it was the home team that was closest to taking the lead in the first quarter of the match, when Jacob Ondrejka twice came to a fruitless finish after effective adjustments.
Then it was even - and fixed situations came to be crucial.
Nicolas Stefanelli pushed the ball into goal after a corner and gave AIK the lead - but the equalizer came just minutes later after an Elfsborg corner, where Gustav Henriksson steered the ball.
The second half had barely started before AIK regained the lead through Benjamin Mbunga Kimpioka.
But Elfsborg would take advantage of their fixed situations.
2-2 came after a corner and awkwardly enough for AIK, Stefanelli was the one noted for the goal.
The club's top scorer Nabil Bahoui, who has been a question mark due to injury, was then replaced with a quarter left but could not raw on the equalizer.
In the next round, AIK will receive Kalmar at home while Elfsborg will visit Hammarby.