With the win, the team is three points and eleven goals ahead of Kalmar FF in second-to-last place, which means direct relegation, ahead of the final round.
IFK Värnamo also left the qualifying spot – but only for a couple of hours. After Halmstad's upset win over Djurgården, Värnamo is back in the qualifying spot.
In a tight bottom struggle, IFK Göteborg and IFK Norrköping are also involved in the battle to avoid qualifying.
Värnamo broke a five-match winless streak and took their first win in six weeks.
The Småland team led the match against BP, who had already secured a new contract, and created several sharp chances.
Simon Thern hit the crossbar before scoring 1–0 via the post in the 36th minute.
After the break, the team had more chances to extend their lead, but it didn't matter this Sunday afternoon as BP didn't have a single shot on goal.
Our defensive play today is magnificent. I think we have a fantastic first half, we dominate a lot, find good spaces, and are dangerous up front. In the second half, it's just about fighting for all three points, says defender Emin Grozdanic.
Värnamo will meet Elfsborg in the final round and Grozdanic is counting on a full house at Finnvedsvallen.
It's going to be great fun, it's about taking three points. All 3,000 who live in Värnamo must come and bring all their cows and sheep too, says Värnamo defender in Max.
BP was injury-plagued and lacked goal king Nikola Vasic, who leads the top scorer list in Allsvenskan with 17 goals.
- Halmstad: 33 points, –14 in goal difference.
Matches remaining: AIK (home).
- IFK Göteborg, 31 points, –9.
Matches remaining: Mjällby (away).
- IFK Norrköping, 31 points, –20.
Matches remaining: AIK (home), Djurgården (away).
- IFK Värnamo, 30 points, –10.
Matches remaining: Elfsborg (home).
- Kalmar FF, 27 points, –21.
Matches remaining: Häcken (home).
- Västerås SK, 20 points, –18 (relegated).
14th place means qualifying against the third team in Superettan in a two-legged tie (home, away). 15th-16th place means relegation.