Nazem Kadri had a goal and an assist, and Darcy Kuemper made 26 saves for Colorado (46-14-6), which has lost two of three.
The Avalanche are 10 points ahead of the Calgary Flames for first in the Western Conference.
"I like the way our team played," Colorado coach Jared Bednar said. "I liked it a lot. I thought it was a good hockey game. I thought our checking game was really good, didn't give up a lot against a dangerous offensive team. Created quite a bit. Didn't finish our chances, obviously took us a long time to get on the board after creating some pretty good chances. Didn't shoot the puck well. But yeah, I liked our game, though. It was a good game for our guys."
Hartman tied it 2-2 at 14:33 of the third period. Zuccarello won a battle with Mikko Rantanen along the right-wing boards and tried to send a pass to Hartman for a tap in. Although his initial attempt was blocked by Devon Toews, the puck came back to Zuccarello, and he quickly passed again to Hartman, who redirected it into an open net.
Kirill Kaprizov gave the Wild a 1-0 lead with a power-play goal at 18:07 of the second period. He scored on a one-timer from near the right post after receiving a backhand pass from below the goal line from Hartman.
Kaprizov has scored 81 points (36 goals, 45 assists) this season, two shy of tying Marian Gaborik (83 in 2007-08) for the most in Minnesota history.
"To me, personally, it's not something I focus on," Kaprizov said. "It's not something I think about. If I beat it, great. I'd be very happy and honored to do that. But for the most part, I'm focused on the game, doing the best I can and getting wins. If I do that, and our team wins, everything will kind of work out. It would be a great accomplishment."
Kadri tied it 1-1 at 6:21 of the third. He won a face-off back to Toews before scoring on a one-timer from the top of the left circle off a pass from J.T. Compher.