Lulea were two points clear of Farjestad as they travelled to Karlstad, and their hopes of retaining their lead were in the balance midway through the third period.
Oskari Laaksonen's opener in the first period gave the visitors the lead, which was cancelled out in the second by Magnus Nygren.
But two goals in less than two minutes of play from Linus Omark and Isac Hedqvist swung the match in Lulea's favour, before Brendan Shinnimin sealed the victory with a little over five minutes remaining.
The three points moves Lulea onto 89 points with three rounds of regular season action to go, and have closed the gap to Brynas at the top to nine points.
The league leaders failed to secure top spot as they were soundly beaten at home by Vaxjo.
Aiming to secure a place in the top 10 and still in the hunt for a top six finish, Vaxjo came flying out of the blocks and led 3-0 by the end of the first with goals from Karl Henriksson, Elias Rosen and Hugo Gustafsson.
It then became the Dylan McLaughlin show in Gavle - the American scored a hat-trick in a 10-minute spell either side of the end of the second period to give the away side a 6-0 advantage.
Consolation goals from Oskar Lindblom and Christian Djoos narrowed the gap, before Emil Sylvegard added Vaxjo's seventh.
Despite a fourth loss in seven, Brynas will become the first newly-promoted side to top the regular season standings if they gain one more point, while they still could still achieve that even if they lose their last three.
Rogle hitting their stride at the right time
The SHL's in-form team in Rogle, whose 3-0 win at fourth-placed Frolunda was their fifth in succession, four of which were secured in regulation time.
After a goalless opener at the Scandinavium, Linus Sandin, Michael Kapla and Dennis Everberg did the damage for the visitors, for whom Arvid Holm made 17 saves in the shutout win.
The good spell is vital for Rogle, who are holding onto sixth place in the standings, one point clear of Skelleftea.
But at least they are now guaranteed postseason hockey this year, as the win secured a 10th-place finish at least.
Skelleftea needed a shootout to beat Timra, who themselves have fallen out of form and are only two points ahead of Rogle.
Elsewhere, Orebro beat Leksand 4-3 as the two remained tenth and ninth, respectively, and another loss for Malmo - this time 3-0 against Linkoping - means Orebro have opened up a four-point cushion in the final playoff place.
In the battle of the bottom two, HV 71 beat Modo 3-1 away from home to cut the gap between the pair to three points.
