The win means that Halmstad has six points down to the qualifying spot and a whole eight points to the relegation line with only three rounds left to play. HBK moved up three places in the table, from 13th to 10th place.
Halmstad started best and put hard pressure on the home team, which had two wins and one draw in the last three matches.
Juhani Pikkarainen became the unfortunate one in a stressed and nervous home team when he steered in Villiam Granath's cross pass on Rami Kaib's pass into his own goal after just over a quarter of an hour.
The home team came back, took control and created some hot chances.
Without getting a full hit.
Dijan Vukojevic, four goals in the last three matches, had two heading opportunities, one straight at Halmstad goalkeeper Tim Erlandsson and one just outside.
Marcus Rafferty had a shot just outside and Erlandsson almost made an own goal when he got a bad touch on a clearance, but Rami Kaib appeared as a saving angel and cleared on the goal line.
Second-to-last Degerfors is still two points behind Öster on the qualifying spot and six points behind Norrköping, just above the qualifying line.
Degerfors will meet Öster away in the next round.
