Leo Carlsson and Alex Killorn each had a goal and an assist, and John Gibson made 34 saves for the Ducks (10-14-0), who trailed 3-1 after the first period.
Gibson played his 448th game for Anaheim, passing Jean-Sebastien Giguere for most by a goalie in franchise history.
Bowen Byram scored two goals, and Ivan Prosvetov made 34 saves for the Avalanche (15-6-2), who have lost consecutive games.
Byram finished off a 3-on-2 rush with a wrist shot from the slot to give the Avalanche a 1-0 lead 36 seconds into the game.
Byram scored again on a 2-on-1 rush for a 2-0 lead at 8:59 of the first.
The Ducks cut it to 2-1 at 14:05 on the power play when Ryan Strome centered a pass through the top of the crease to Adam Henrique, who redirected the puck into the net.
Devon Toews scored with a wrist shot from the right circle to make it 3-1 with 43 seconds left in the first.
Carlsson scored from the slot off a backhand feed from Killorn to cut the lead to 3-2 at 2:58 of the second period.
Killorn scored his 200th NHL goal with a wrist shot from the right circle with two seconds left on a power play to tie it 3-3 at 10:22 of the second period.
