Brynas looked to have the advantage in the series, having won game four 5-3 on the road and with the chance to retake the overall lead on home ice, but they were second best in Gavle last night.
Brian O'Neill was the architect of the opening goal, which the visitors scored inside the first 30 seconds. He won the puck back behind the Lulea goal, found Isac Hedqvist, who then returned the favour for O'Neill to score from close range.
Lulea then delivered a sucker-punch right at the end of the first period, doubling their lead with O'Neill and Hedqvist involved again to set up Marcus Hardegard to power past Ludwig Persson.
The lead stretched to three goals midway through the match, as Linus Omark latched onto a loose puck and held off the defence to score his second goal of the Finals.
But whatever the Brynas coaches said to their players ahead of the third period, it had the desired effect as the home side scored their first goal 38 seconds after the restart. From behind the Lulea goal, Christian Djoos picked out Greg Scott, who applied the simple finish.
The comeback was truly on less than five minutes later, when Victor Soderstrom cut the puck back for Oskar Lindblom, who squeezed it past Matteus Ward.
But the home side could not find that crucial equaliser, instead, two quickfire goals in the next three minutes killed off the match in Lulea's favour.
O'Neill grabbed his second of the match, poking the puck beyond Persson from behind the net, before a fine individual goal from Markus Nurmi, who won the puck back at centre ice and raced away to score.
In the final minute, Lulea finally took advantage of a flurry of powerplays they were awarded, and Mathias Brome was on hand to complete the 6-2 victory.
It marks the second time in a row and third time in the series that the away side has come away with the win; if Lulea can buck that trend at Coop Norrbotten Arena on Thursday in game six, they will be crowned champions of Sweden.