Minnesota had lost each of its first five previous trips to Colorado and appeared headed in the same direction in this one. But Laaksonen tied the game, putting in a rebound past goaltender Patrick Roy.
After Willie Mitchell's slap shot hit the left goalpost, Laaksonen breezed past several defenders and caught Roy out of position.
Laaksonen's tally came just over three minutes after Pascal Dupuis converted a breakaway, cutting Colorado's lead to 3-2.
Roloson faced intense pressure in overtime, stopping five shots in the extra session. At 3:56, he turned aside Adam Foote's one-timer, and nearly two minutes later he robbed Alex Tanguay from inside the right faceoff circle.
Defenseman Eric Messier recorded his first career multi-goal game and offseason acquisition Jeff Shantz also scored for Colorado, which is 9-1-1-0 all-time against Minnesota.