The first half offered a cavalcade of chances, and Alexander Jeremejeff, Tobias Sana and Oscar Uddenäs each had a free position.
But it was substitute Dane Mikkel Rygaard who broke the deadlock after Valgeir Fridriksson's intervention, and thus scored his sixth goal of the season.
Värnamo were not uneventful, but Häcken continued to create the sharpest chances.
Jeremejeff's super season continues
And if there is one thing you can be sure of this season, it is that sooner or later Jeremejeff will score if the chances arise.
So too this afternoon when he hammered home 2-0 in the 55th minute, scoring his 20th goal of the season.
Before the games ended, Ibrahim Sadiq managed to score both one and two goals, and Wenderson scored a consolation goal for Värnamo, which resulted in a 4–1 total.