A win on the final day of the regular season had lifted HV 71 above their play-out opponents, giving them home advantage in four matches should the series to go seven games.
They set about making full use of that advantage, taking the lead in the dying seconds of the opening period when Hugo Fransson teed up Justin Kloos to score the series' first goal.
Having gone on a brilliant run to give themselves hope of avoiding the play-out, Leksand then saw those hopes dashed with successive defeats to end the regular season, and their recent form got worse with five minutes to play in period two, when Martin Johnsen put HV 2-0 ahead.
Late in the second, Riley Woods was called for high-sticking, and despite the break in between periods seriously testing their patience, Leksand got themselves on the board through Michael Lindqvist in the first minute of the third, with time winding down on the powerplay.
But even with 19 minutes to play with, Leksand were unable to force a late leveller, meaning the Jonkoping side win the first game 2-1 and have the chance to seriously boost their survival bid when they host game two on 20th March.