The Avalanche remained two points behind the St. Louis Blues for the division lead; the Blues defeated the Anaheim Ducks 4-2.
Pavel Buchnevich tied the game for the Rangers with 13 seconds left in the third period and goalie Alexandar Georgiev pulled for an extra attacker. New York hadn't tied a game in the final minute of the third period since April 5, 2019, when Buchnevich scored with seven seconds remaining against the Columbus Blue Jackets.
WATCH: [All Rangers vs. Avalanche highlights]
Compher won it for Colorado when he tipped in a shot by Cale Makar, who had three assists in his first game after missing five with an upper-body injury.
"It's kind of a blur," Makar said. "Their guy screened their goalie, I just threw it to the net and I saw [Compher] was going there. He got a great stick on it, put it over his shoulder, I think. I didn't really see the puck go in, but it was a great tip by him."
Tyson Jost and Vladislav Namestnikov scored, and Pavel Francouz made 30 saves for the Avalanche (42-20-8).
"I thought it was special teams and goaltending, that's what it was," Colorado coach Jared Bednar said. "I thought we were not good 5-on-5, which is usually the strength of our game. Penalty kill was excellent; I thought those guys did a real nice job again and I thought we had some guys play real hard, log a lot of minutes, way more than they normally do.
"On the defensive side, I thought we were terrible. [Francouz] was awesome and we got the win, and we'll take it."