Having been cut adrift at the bottom of the standings, eight points from their last three games has moved Leksand to within four points of 12th-placed Orebro and guaranteed survival with seven regular season matches to play.
Three wins in a row is their best run of the season, surpassing their two wins in the opening two rounds in September, the only previous time they strung a pair of victories during this campaign.
The only goal of the game came in the 13th minute of the second period, when Alexander Lundqvist played a long pass straight down the centre, bisecting the Linkoping defence, to play Lukas Vejdemo through on goal. His initial effort was saved, but he made no mistake with the rebound.
Hosts Linkoping were relentless in the final period in search of an equaliser, but despite two powerplaysand 17 shots on goal, they failed to find a way past Filip Larsson, who made 34 saves across 60 minutes in total to record the second Leksand shutout in as many games.
A roughing call at the final buzzer led to tensions boiling over, as three players per team were ejected for unsportsmanlike conduct, but there was no changing the 1-0 final score.
It's four losses in a row now for Linkoping, who sit 11th, five points clear of the relegation playoff zone.