Dwayne Roloson made 39 saves to lead the Wild in Game One of their Western Conference quarterfinal series.
The Wild, winless in eight previous visits to Colorado, entered their inaugural postseason with a splash, scoring three goals in a 4:20 span of the second to take a commanding lead.
Defenseman Filip Kuba converted a power play 5 1/2 minutes into the period for the first playoff goal in team history. Gaborik followed with a power-play tally 3:55 later, and Walz netted his fourth career postseason goal to give the Wild a 3-0 cushion.
Roloson withstood an 18-shot attack in the first period before making 21 saves the rest of the way for his first playoff win since 1999 with Buffalo.
Andrew Brunette also scored for Minnesota, which finished the regular season with an NHL-best 31-4-1 record when netting the first goal of the game.
Game Two is Saturday at Colorado's Pepsi Center in Denver.