The teams will play again here Sunday.
John Gibson made 33 saves for Anaheim (12-22-7), which is 1-3-1 in its past five games.
"I was impressed with our effort and attention to detail," Ducks coach Dallas Eakins said. "But still, we'd like to get on the other side of that game."
Gibson has allowed one goal three times in his past four starts.
"He quietly went about his business," Eakins said of Gibson. "When needed, he was there to answer the bell."
Anaheim went on its first power play at 13:08 of the second period, but Cam Fowler and Jakob Silfverberg of the Ducks were called for holding penalties over the next 1:07, wiping out the power play and giving the Avalanche a brief 5-on-3.
The Ducks killed the penalties, but Nichushkin gave the Avalanche a 1-0 lead shortly afterward.
Nichushkin got open in the slot and scored on a one-timer off a feed from Ryan Graves at 17:12.
Rantanen scored his Colorado-leading 23rd goal of the season into an empty net to make it 2-0 with 34 seconds left.
"I didn't think that we had a lot of jump tonight," Bednar said. "It seemed like our energy was on a little bit on the low side, but we did get better as the game went on."