Adam Henrique and Mason McTavish scored 24 seconds apart in the third period, and John Gibson made 41 saves for the Ducks (15-29-5), who have won three of their past four games and finished 3-2-1 on a six-game road trip.
"This was a huge game for us," Anaheim coach Dallas Eakins said. "I'm not so sure about them, but we talked before the game about [how] we don't have to beat these guys four times in two weeks. We just have to beat them tonight, and that was going to be our measuring stick.
"We wanted to be above .500 on this road trip. We were able to accomplish that. But I think the biggest thing is our team beat the Stanley Cup champions, and we had to do it with a whole lot of sandpaper and hard work. And our guys should be proud of that."
Mikko Rantanen scored twice, and Samuel Girard had a goal and an assist for the Avalanche (26-18-3), who had won six straight. Pavel Francouz made 27 saves.
"I really liked our first two periods," Colorado coach Jared Bednar said. "There's some habits that are creeping in our game though, whether it's for five minutes, 10 minutes, 15 minutes. I just don't like getting outworked for stretches that cost you hockey games, and that's what it was.
"Let's call it what it is; the intensity that they came out with in the start of the third period and what we had was not comparable. If you look back on it, it doesn't surprise you that you let the game slip away, and we're too deep in the season now for that to happen."