The Avs, who swept the Los Angeles Kings in the first round, wasted no time in racing out to a 3-0 lead in the first period.
Sam Malinski opened the scoring when he received a pass from Martin Necas before firing it home.
The top seed in the Western Conference doubled their lead less than a minute later through Jack Drury, who benefitted from a giveaway from the Wild as he swept his shot past Jesper Wallstedt.
There was no stopping the Avalanche's onslaught, as they added a third moments later via Arrturi Lehkonen, who made the most of his side's power play by fininshing off Nathan MacKinnon's excellent play to send the home fans into jubilation.
It was starting to look like Minnesota would be in for a beating at the Ball Arena. With the hosts outshooting them 16-9 in the opening frame, the Wild were in danger of scoreline geting out of hand.
With five minutes left before intermission, the guests got on the board. After a battle for the puck by the boards, it ultimately fell to Marcus Johansson, who finished from close range.
A minute later, and it was 3-2! It all came from a gorgeous backhand pass from Quinn Hughes, who set up Ryan Hartman in front of the goal. The centre converted his chance, and just like that, the Wild were behind by one.
The scoring picked back up 4:16 into the second, when a Colorado breakaway saw Valeri Nichushkin find Nick Blankenburg to beat Wallstedt.
This game had everything, and although they were down by three goals early on, the Wild managed to take the lead during the second with three goals of their own.
Vladimir Tarasenko received pass from Yakov Trenin to race in on goal. Facing Scott Wedgewood, the 34-year-old kept his composure by making a move and finishing with precision.
After Hughes tied things up later on in the period, as he was the one to get a stick on Danila Yurov's shot.
The Wild were left shorthanded after Brock Faber was caught for hooking. Yet, they found a way to take the lead. After the Avs coughed up the puck, Marcus Foligno made the most of the error, going the other way before scoring to give his side their first lead of the night.
With how this game has already gone, it was inevitable that would not be the last goal. It took Colorado 69 seconds to restore parity. Just as the Wild killed the power play, Devon Toews shot into traffic, which took a deflection before flying in.
The third period was where the home team pulled away. Cale Makar got in on the scoring when he was afforded too much space on the right wing. His shot gave Wallstedt no chance as the Avs went back in front.
Nazem Kadri made it 7-5 after Ross Colton fed him in from a blocked shot. The former was completely open, as he finished off his chance with deadly precision.
It looked like Colorado had finally found daylight in the contest, only for Mats Zuccarello to make things a nervy finish for them. A pass from Matthew Boldy appeared to cause some confusion in front of the goal. Zuccarello made the most of that by tapping it in from close range.
In the end, the Avalanche were able to get over the line. Makar got his second of the night when he fired from the right wing into the back of the net, with traffic in front of the goal.
MacKinnon added an empty netter with 2:08 left as the Wild could not fight back this time around.
Thirteen different players for the Avs collected a point in the game, while 11 did so for the Wild, reflecting the chaotic nature of the contest.
Colorado take a 1-0 lead heading into second game of the series, which will occur on Tuesday night.
