BP initiated the goal scoring at Strawberry Arena, when Alex Timossi Andersson nodded in Wilmer Odefalk's fine pass.
Before the half-time whistle, AIK had turned the tables. First, the home team equalized after a collaboration between the team's top scorer Rui Modesto and Ioannis Pittas.
In added time, Anton Salétros scored the 2-1 goal via a free kick.
We are extremely disappointed after the first half, we look like a junior team. I don't think it's a good match from us, we can do better, so I'm extremely disappointed, says BP's Ludvig Fritzson in Max.
AIK now climbs to fifth place, one point ahead and with one more match played than sixth-place Häcken. BP lies in tenth place.
Earlier in the week, IFK Värnamo fired coach Anes Mravac. At the same time, Ferran Sibila was presented as the new coach.
In Sibila's first match as Värnamo coach, it ended in a draw against BK Häcken at Bravida Arena, and a valuable point in the relegation battle.
The home team started best, and Jeremy Agbonifo scored his first Allsvenskan goal after 27 minutes.
In the second half, Värnamo came more into the match. And after Gustav Engvall was fouled in the penalty area, the visiting team was awarded a penalty, which Ajdon Zeljkovic converted in the best possible way.
I always want to win, but a point is fair. They had more chances in the first half, we had more in the second, says Sibila after the match.
After today's 1-1 result, Värnamo remains in the relegation spot, Häcken in sixth place.