The first two matches in the series had been won by the away side, with Orebro winning game two in convincing style at Vaxjo's Vida Arena, 4-1 on Saturday.
But 18 minutes into a tight opening period, Vaxjo broke the deadlock when Emil Larsson won possession in the attacking zone and scored unassisted.
Tempers flared more than once in the second period with players from both sides serving time in the penalty box, and despite plenty of Orebro pressure, they could not force an equaliser.
In the third period, it was the Lakers who looked the more likely to score the second goal, forcing Orebro to risk everything at pull the goaltender.
It backfired not once, but twice in the final 90 seconds, and both times it was Hugo Gustafsson who applied the empty net finish - first by skating down the ice to tap home, then by shooting from the centre line.
Emil Larmi registered a shutout in the 3-0 win, helped by his defence allowing only 17 shots on goal in the match, as last year's semi-finalists Vaxjo booked another last eight place.
SHL Quarter-finals
Vaxjo join Malmo in the Quarter-finals after the Redhawks' 2-0 series win over Rogle, thus the draw for the round is as follows:
Brynas and Lulea will host the first games of their respective series on Thursday March 20th, with the other two series beginning the following day.