The Avalanche outshot the Wild 12-5 in the first period, but it was the home team that found the back of the net first
Mikael Granlund began the scoring at 7:48 of the first period, as he took a behind-the-net pass from Eric Staal and fired a close-range wrist shot near side past Bernier. The tally came on the power play and during a delayed Avs penalty, allowing Minnesota to have a two-man advantage on the ice.
The Wild extended its lead to 2-0 during another power play as Matt Dumba's slap shot from the point found twine 2:27 into the middle frame.
The Avalanche quickly answered with Agozzino tallying off a rebound while driving to the front of the net just 2:12 after Dumba's goal.
Rocco Grimaldi began Colorado's scoring sequence by streaking down the right-wing side with the puck before getting tripped up by a Minnesota player. His momentum forced him to slide into netminder Devan Dubnyk, while the puck caromed off the goalie and right to the stick of Agozzino.
The play did not go to a video review for goaltender interference.
Rookie Andrei Mironov picked up an assist on Agozzino's first goal of the preseason.
The Avalanche had its chances to tie the contest over the remaining two periods. It had six more power plays in the final 30 minutes of regulation, including several 5-on-3 opportunities, but couldn't capitalize on the chances.
Colorado finished 0-for-8 with the man advantage while the Wild went 2-for-5.
Dubnyk made 28 saves for the Wild, which was outshot 29-24 by the Avs.
The two clubs meet again on Sunday in Denver at 5 p.m. MT. It will be the second of three-straight preseason games for the Avalanche, who also plays at the Dallas Stars on Sunday.