In a thrilling clash between the country's top two sides in Gothenburg, the hosts grabbed the lead in the first half when, from a corner, Tomas Olsson steered team mate Erik Lund's shot into AIK's goal with his chest.
AIK equalised in the second half when striker Martin Mutumba beat Lund and set up unmarked Brazilian Antonio Flavio, who fired the ball past keeper Kim Christensen.
AIK captain Daniel Tjernstrom was the hero when he controlled a chipped pass by Liberian Dulee Johnson inside the penalty box and calmly slotted the winner.
AIK, who will go into the qualifying rounds of next season's Champions League, will face IFK Gothenburg again in the Swedish Cup final next week.
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