Leksand must take at least one away win to stand any chance of staying in the SHL, and their hopes of doing that were raised in the ninth minute, when Oskar Lang broke the deadlock.
But Pettersson made his mark on the game in the final three minutes of the opening period - first, he was perfectly place on the left wing to fire home following patient build-up on a powerplay, before turning the match around with another in the final minute.
HV had the better of the second period, but had to wait until four minutes into the third to open up a two-goal lead, as Andreas Borgman scored his first goal since the sides met at Leksand two weeks ago in the regular season.
Lukas Vejdemo pulled one back for the visitors with five minutes to play, but that wasn't enough to stop Leksand from falling to a 3-2 defeat, their fourth loss in a row, as the Jonkoping side moved onto as many victories in succession.
The series now moves to the Tegera Arena, where Leksand must win at least one of their two home games. Game three takes place at 18:30 CET on Sunday 22nd March.