The series now heads to a Game 7, back in Denver on Wednesday night.
It was Pominville's first goal of the playoffs. Then Marco Scandella hit the back of the empty net for good measure to put the game away for Minnesota.
The Wild brought a lot of energy onto the ice as a quick rush allowed Minnesota to build an early lead.
Then just over the midway point of the first, Mikael Granlund gave Minnesota a two-goal lead with his second playoff-goal. Pominville assisted to pick up his fourth helper of the playoffs.
Down 2-0 and immediately after a two-man advantage expired for the Wild, Colorado's Ryan O'Reilly found Paul Stasny, fresh out of the box, and hit him to set up a breakaway goal to cut the Wild lead to 2-1, with a short-handed goal.
Then early in the second, the Avalanche scored on a power play goal from Nick Holden to even the score at two.
Colorado had a couple of chances, but Darcy Kuemper turned the Avalanche away. He finished with 21 saves.
It stayed that way until late in the third when Parise tipped in the go-ahead goal, his second goal of the night to put the Wild back on top at 3-2. Koivu and Suter teamed up to assist.
Avalanche coach Patrick Roy pulled goalie Semyon Varlamov with 2:44 to go, and the Wild finally took advantage of the empty net on the goals from Pominville and Scandella.
The series will now shift back to Denver for Game 7, on Wednesday night. The winner advances to the Western Conference Semifinals to face the Chicago Blackhawks.