Frölunda scored the first goal of the match at the beginning of the second period when they had a five-on-three advantage.
Goalkeeper Jesper Wallstedt and Juhani Tyrväinen had each taken an unnecessary expulsion and scored Joel Lundqvist's goal.
Tyrväinen was then behind Luleå's turn.
First he was involved in playing Konstantin Komarek's equalizer and then he made it 2-1 there.
But Frölunda came back.
Patrik Carlsson made it 2-2 in his 400th SHL match of his career when he came free with Wallstedt.
It was a match where goalkeepers Wallstedt and Matt Tomkins impressed.
It also went all the way to penalties.
Once there, Luleå won after, among other things, a nice penalty by Komarek.
The home team put all their penalties and the decisive one put Jack Connolly.