Nazem Kadri had two goals and two assists for Colorado. Philipp Grubauer stopped 15 shots after replacing Hunter Miska, who allowed four goals on seven shots.
''Hunter would like to make another save or two in the first period, but I think we hung him out to dry,'' Avalanche coach Jared Bednar said. ''It's not something you want to do with a young goaltender who's coming in and trying to build some confidence.''
Anaheim had two goals in its previous three games but broke out with a big first period. Adam Henrique led with a goal and two assists, and Troy Terry also scored but the Ducks couldn't sustain a fast start.
Anaheim captain Ryan Getzlaf put blame on himself and linemates Rickard Rakell and Maxime Comtois.
''Unfortunately, a lot of it had to do with our line. We're going to wear this one for our team,'' he said. ''I thought our guys did a great job going out and getting momentum at different times and it seemed like every time we stepped on the ice it was in our zone or in our net, so we've got to look at our game and accept responsibility for that.''
The teams combined for six goals in the first period - four in the opening 7:02. Andre Burakovsky gave Colorado a 1-0 lead at 1:01, but the Ducks scored on their first two shots, by Terry and Danton Heinen. Kadri's first of the night made it 2-all.
Miska, who gave up five goals in his last game, an overtime loss to Anaheim 10 days earlier, struggled against the Ducks again. When Henrique scored at 15:59 to give Anaheim a 3-2 lead, it was just the fifth shot Miska faced. Then, after Derek Grant was awarded a penalty shot when he was tripped on a short-handed chance, Miska was beaten again with 17 seconds left in the period.
''It was first hot, then cold,'' Mikko Rantanan said in describing Colorado's up-and-down night. ''You give confidence to the other team, and a 4-2 lead and they're a little happy - and then we score six in a row. First hot, then cold.''
Grubauer came on to start the second and stopped all seven shots he faced in the period. That allowed the Avalanche to tie it on goals by Rantanen at 11:25 and Kadri's second, a deflection in front of Ryan Miller, at 18:26.
The goal by Rantanan came on a backhand off Miller's back, nearly identical to the one he scored against the goaltender 10 days earlier.
''I tried to do that, I'm not going to lie,'' he said.
MacKinnon scored a power-play goal 1:01 into the third and Girard made it 6-4 at 3:24.
Miller had 28 saves.
''It was an even game on the road against a top team and we just needed to get a kill going in to start the period and go back to a simple, boring game on the road,'' Anaheim coach Dallas Eakins said. ''The goal to start the period near the end of the penalty kill wasn't great, and we just couldn't sustain their pressure.''
Pierre-Edouard Bellemare scored into an empty net at 16:48 and Brandon Saad added a power-play goal at 18:45, his 10th of the season.
NOTES: Devon Toews and Joonas Donskoi had two assists each for Colorado. ... Anaheim G John Gibson is day-to-day with a lower-body injury. ... Avalanche D Bo Byram and C J.T. Compher, both out with lower-body injuries, skated Tuesday morning and could return Thursday. ... Ducks F Jakob Silfverberg went off in the first period after blocking a shot but returned later.
Ducks: Host the Arizona Coyotes on Thursday night.
Avalanche: Host the Minnesota Wild on Thursday night.
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