The Coyotes took a 2-1 lead at 10:34 of the second period on a goal by Goligoski after a turnover by Avalanche forward Tyson Jost. Clayton Keller passed across to Goligoski in the left face-off circle for a shot over the right arm of goalie Semyon Varlamov, who had 24 saves.
Crouse, who was recalled from Tucson of the American Hockey League on Tuesday, scored his first goal of the season at 15:35 of the third period to make it 3-1 after taking a return pass from Josh Archibald.
"It was a little bit of a fluke," Crouse said. "The puck kind of hit me in the arm, and I just started skating and before I knew it the puck was right there. I made a one-legged pass to [Archibald], and he made a heck of a pass back to me and I just had to put it in the empty net."
Matt Nieto shot off the right post at 2:05 of the third period, Raanta stopped Nathan MacKinnon on a breakaway at 5:10, and Nikita Zadorov hit the crossbar at 12:55.
"We should have scored at least a couple goals there, and their goalie played pretty well," Rantanen said. "Everyone knows it's one we should have had. Three points out of a playoff spot, we can't lose these games, especially at home."
The Avalanche killed a 5-on-3 power play that lasted 1:53 after Nieto and Erik Johnson took consecutive delay of game penalties in the final minute of the first period. They killed all four Coyotes power plays and have killed 27 in a row in the past nine games.
"If the rest of our game played with the same urgency, we'd be a lot more successful," Bednar said.
Rieder gave the Coyotes a 1-0 lead 54 seconds into the game. Brendan Perlini was carrying the puck behind the net when Johnson poked it to the side, and Rieder scored into an open net.
"Luckily, it bounced on my stick," Rieder said.
Rantanen tied it 1-1 at 3:56. Johnson sent a long pass to Rantanen, who skated to the left circle and shot over Raanta's right shoulder.
