Kane took a pass from Dylan Larkin and beat Colorado goalie Justus Annunen from the slot. Larkin tied it 1-1 at 12:02 of the third period on the power play.
Alex Lyon made 28 saves for the Red Wings (30-20-6), who have won three in a row.
Nathan MacKinnon scored for the Avalanche (35-18-5), who had won two in a row. Annunen made 28 saves.
MacKinnon gave Colorado 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.
Jake Walman had a chance to tie it on a breakaway at 15:34 of the second period, but shot over the net.
Larkin broke up Annunen’s bid for his first NHL shutout after tying it in the third.
Logan O'Connor was called for holding Ben Chiarot with 1:09 remaining in the third, but Annunen made a point-blank pad save on J.T. Compher with eight seconds left in regulation.
Colorado killed the remainder of the power play in overtime, but Lyon stopped Bowen Byram on a breakaway 36 seconds before Kane’s goal.
