As the only team in the top five in action this weekend, Elfsborg had the chance not only to boost their title hopes, but record back-to-back wins for the first time since May.
But their inconsistent form looked to be going nowhere in the first half, as Hacken created plenty of chances, with Severin Nioule and John Dembe guilty of not taking some of the better ones.
The hosts' dominance didn't diminish early in the second half, with Isak Brusberg and Dembe forcing excellent saves from teenager Simon Eriksson.
Having soaked up all the pressure, Elfsborg took the lead with 15 minutes to go - Arber Zeneli's cross found Per Frick, and his header back across goal looked to be going in, but Ari Sigurpalsson made sure with an outstretched leg.
With three minutes to go, the visitors dealt Hacken a crushing blow, when Zeneli tried to slip a ball through to Frode Aronsson. The pass was blocked back to Zeneli, so he took it upon himself to curl the ball into the top corner and secure the win.
Deep into added time, the Getingarna finally found a way through when Dembe headed home Amor Layouni's cross, but it was too little too late who are now winless in three and sit 10th.
Djurgarden saw their two-match winning run come to an end as they were held at home, 1-1 by Halmstad.
The Jarnkaminerna were given a helping hand midway through the first half when goalkeeper Tim Erlandsson palmed the ball above his head but could not prevent it dropping into his own net, but Halmstad regrouped quickly and were level five minutes later through Villiam Granath's header.
Eight minutes from time, Halmstad again did a good impression of wanting to help their hosts out when Rami Kaib was sent off for a second bookable offence, but Djurgarden could not force a winner. They sit seventh, while HBK remain 12th and without a win in four.
Also on Sunday, Sirius and Oster played out a 1-1 draw which saw Degerfors drop below both and into the bottom two ahead of their meeting with Goteborg tomorrow.
Leo Walta broke the deadlock from the penalty spot as the match entered its final quarter, but the Uppsala side could not hang on and five minutes later Vladimir Rodic equalised shortly after coming on.
Both sides - plus Degerfors - sit on 14 points. Oster have picked up successive draws, while Sirius ended a run of four straight defeats, but both remain without a win in six.