It is tight under Malmö FF in the Allsvenskan table top and at home at Hisingen, Häcken wanted to climb a few pin holes with four rounds left.
Östersund came to visit and Viktor Lundberg gave Häcken the lead with a precise cross, his first goal of the season, in match minute 13.
However, the visitors played their way up in the second half and strong Blair Turgott nodded in his fourth goal in four games a quarter after the break.
ÖFK had momentum, but when 2-1 came it was Häcken who set it.
Rasmus Lindgren met a corner with his head and decided in the 83rd.
Häcken climbs up to third place in a limping table, while Östersund is still eleven.
The team has three matches left to play.