Goodrow tied it 1-1 at 18:06 scoring at the side of the net off a pass from Jacob Trouba.
"A give-and-go and Blais made a great pass right to 'Troubs,' and Troubs made a great pass right over to me," Goodrow said.
The Avalanche went 4-for-4 on the penalty kill, including the final 1:39 of overtime after MacKinnon was called for hooking Panarin, who had a breakaway and was stopped by Georgiev.
"I thought our penalty kill was really good tonight, which is nice for to see our guys get rewarded," Avalanche coach Jared Bednar said. " … They created a few chances, and when we needed a save, Georgie was there. But overall, a good night from our penalty kill, and they get a big short-handed goal for us, which was huge."
Georgiev made 19 saves in the third period and overtime.
"A lot of great memories (in New York)," Georgiev said. "A lot of great players and the staff. Tried to think about positives, and there were a lot of those. … I would say a pretty memorable [win]. I'll try to enjoy this one tonight, but then recharge. We've got a lot of other really important games coming up."
NOTES:Avalanche defenseman Devon Toews returned after missing two games with an undisclosed injury. He had six shots on goal in 26:26 of ice time. … Colorado has won four straight against New York and five of the past six. … The Rangers won 56 percent of face-offs, led by center Vincent Trocheck, who won 15 of 19. … The Avalanche, who lead the NHL on the power play (50.0 percent), have scored at least one with the man-advantage in six of their seven games.