Travis Boyd, Nick Schmaltz and Michael Carcone scored for the Coyotes (11-9-2), who won their third in a row after losing three straight. Connor Ingram made 28 saves.
Cale Maker had a goal and an assist, Mikko Rantanen had two assists and Nathan MacKinnon and Miles Wood scored for the Avalanche (15-6-1), who had won four straight and seven of eight. Alexandar Georgiev made 29 saves.
Carcone’s wraparound goal gave Arizona a 3-2 lead at 1:08 of the third period. Carcone, playing his first full NHL season, has 10 goals, including four in his past four games.
MacKinnon’s power-play goal tied it 3-3 at 11:04, a one-timer under the crossbar off Makar’s cross-ice pass.
Makar scored on a power play for a 1-0 lead at 19:31 of the first. His shot down the slot from just inside the blue line eluded Ingram as Valeri Nichushkin screened in front.
Boyd tied it 1-1 at 3:03 of the second period. J.J. Moser’s shot from the point deflected off Liam O’Brien’s stick at the hash marks and then off Boyd’s stick and in.
Wood gave Colorado a 2-1 lead at 4:44, picking up the puck in the corner, cutting across the crease and tucking it inside the far post.
Schmaltz made it 2-2 at 16:22 just 11 seconds into a power play with a one-timer from the slot.