That sealed a 4-2 series win in the Semi-Finals and set up a best-of-seven series with Brynas to decide the title.
Needing a victory to stay alive, Frolunda started brightly in front of a raucous crowd at the Scandinavium, but could not force a way through in the first period despite leading the shot count 14-3.
As is so often the way, that lack of efficiency came back to bite in the first minute of the second period, when Anton Levtchi linked up with Markus Nurmi before sweeping the puck past Lars Johansson.
Though Johansson was busy in the remainder in the second, the goal still came against the run of play, as Frolunda continued to be denied by both Matteus Ward and the frame of his goal.
It was a case of deja vu early in the third period, when the home side got caught on the counter attack, and this time Levtchi turned provider for an unguarded Brendan Shinnimin to bury Lulea's second.
A game misconduct penalty against Nicklas Lasu did not help the hosts' cause late on, but however they tried, there was no way past Ward, who made 29 saves to complete the 2-0 shutout victory and complete the series win for a side who only had 11 efforts on goal in the 60 minutes.
Shinnimin came within a whisker of adding a third, but his empty-netter struck the pipes and bounced clear.
Brynas, who beat Skelleftea 4-1 in their Semi-Final series, will host game one of the Finals at 15:15 CEST on Saturday.