Alex Lyon made 30 saves for the Red Wings (30-20-6), who have won three in a row.
Detroit has 18 points (8-14-2) in 24 games when trailing after two periods.
“You don’t win that often when you are trailing going into the third, and you certainly don’t do it as many times as we have this year,” Red Wings coach Derek Lalonde said. “I think that speaks well of our group.”
Nathan MacKinnon scored for the Avalanche (35-18-5), who had won two in a row and three of their past four. Annunen made 28 saves.
“It was a hard-fought hockey game, but I thought [Detroit] was probably the more desperate team in the third period,” Colorado coach Jared Bednar said. “It’s a good road point.”
MacKinnon gave the Avalanche a 1-0 lead at 4:48 of the second period. He took a pass from Mikko Rantanen in the slot and beat Lyon for his 34th goal of the season.
“I thought we created some chances, but we spent too much time in our own end,” Colorado defenseman Cale Makar said. “You can’t do that all night, and some of that is on me. I can’t turn the puck over when we need to get it out of our end.”