Marian Gaborik converted a penalty shot in the second period for the Wild.
Pittsburgh has been outscored, 26-4, for the worst first-period goal differential in the NHL. By the time the power failed in the final minute of the period, the Penguins were facing a 3-0 deficit.
Laaksonen started the scoring at 8:03 when he banked a shot off defenseman Patrick Boileau and past rookie goaltender Marc-Andre Fleury.
Just 37 seconds after Sergei Zholtok converted a perfect cross-ice pass from Pierre-Marc Bouchard at 18:51, Laaksonen capped his second two-goal game of the season.
Gaborik made no mistake after being pulled down from behind by Pittsburgh's Steve McKenna with 5:44 to go in the second.