Ben Chiarot scored, and Jake Allen made 30 saves for Montreal (6-17-2), which has lost two straight since firing general manager Marc Bergevin on Sunday.
"I thought we had some good O-zone time," Canadiens coach Dominique Ducharme said. "Obviously, we wanted to get more pucks [to the net], but … I thought they were pretty composed on the other side defensively, hard battles down low. Five-on-five it was a pretty tight game."
Jeff Gorton, who was hired by the Canadiens as executive vice president of hockey operations Sunday, was on hand for the game.
"I met him a couple of days ago for the first time and he seems like a great person," Montreal center Nick Suzuki said. "He's done a lot of good things with other teams."
Nichushkin gave the Avalanche a 1-0 lead with a shorthanded goal at 3:11 of the second period. Logan O'Connor forced a turnover by Canadiens defenseman Chris Wideman and passed to Nichushkin, who came off the bench and scored with a one-timer that trickled through Allen.
"[O'Connor is] such a puck hound on the forecheck and tracking to turn pucks over and get us back to playing in the other end of the rink," Bednar said. "He's such a strong skater. The penalty kill he's all over the puck and creating turnovers tonight like he did on 'Val's' goal, so he's been invaluable for us."
Chiarot tied it 1-1 with a power-play goal at 6:51.