Malmo missed a penalty and had a goal ruled out for offside as they were held 1-1 by relegated Orebro.
Miiko Albornoz saw his early spot kick saved by Tomer Chenicinski but then made amends by giving the home team a 57th-minute lead.
Orebro equalised 13 minutes later as they stretched their unbeaten run to four games.
Haecken took a 1-0 lead after AIK Stockholm goalkeeper Ivan Turina collided with team mate Martin Mutumba to allow Oscar Lewicki a simple finish.
Icelandic international Helgi Danielsson levelled for the visitors just before halftime and the 1-1 draw extinguished Haecken's hopes of landing their first title.
Elfsborg cruised into a 2-0 lead thanks to Lasse Nilsson and Anders Svensson. Mjallby battled back to 2-2 but Viktor Claesson headed the winner just past the hour.
With one match left Elfsborg top the table on 58 points, two ahead of Malmo and four in front of Haecken.
Victory on Sunday at home to Atvidaberg would secure the crown for Elfsborg.