It was visiting Jukurit from S:t Michel who took a 2-0 lead.
First through the talent Niko Huuhtanen who took over when Pontus Själin dropped the club and then Otto Mäkinen in numerical superiority.
Before the second period was over, Isac Brännström scored the reduction from close range.
Then it was Luleå's turn to be a man more.
At the beginning of the final period, Einar Emanuelsson put a delicious pass to Juhani Tyrväinen, who had to score on his compatriots.
But Jukurit took back the lead.
Jesper Piitulainen got free, faked a shot and rounded Matteus Ward in the Luleå goal.
The chain with Brännström, Tyrväinen and Emanuelsson still continued to impress.
Brännström was strong in front of the box and got the equalizing goal to make it 3-3 through a nice control.
With six minutes left of regular time, 24-year-old Brännström was in front of the goal again and then he scored another goal.
It was also the winning goal.
- I think we play a good match.
We take over the match because and show that we are a better team, says Luleå coach Thomas Berglund.
With the victory, Luleå has won all of its opening three games in this year's Champions Hockey League group stage.
They continue with a home match against Sparta Prague on Sunday.