Juraj Slafkovsky scored two goals for Montreal (33-27-9), including one of its three in the third, when Joshua Roy and Christian Dvorak also scored. Montembeault made 33 saves.
The Canadiens are 3-0-3 in their past six games.
“We always believe, we always want to play hard,” Slafkovsky said. “We don’t want to give anyone anything for free and that’s what we showed today.
The Canadiens, who are 8-1-4 in their past 13 games, are one point ahead of the New York Rangers for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
“It’s easy to roll over, and that’s just not what we do on our team,” Montreal captain Nick Suzuki said. “The guys just kept battling, getting chances. We really took over the game and we could have probably got a few more in the third. So it’s a big point.”
The Canadiens trailed by three midway through the third before Roy cut it to 4-2 at 9:24 by putting away the rebound of Alex Newhook’s shot.
Slafkovsky drew Montreal within 4-3 at 9:54 with a wrist shot past Blackwood from the top of the slot, and Dvorak tied it 4-4 at 13:32 on a backhand past Blackwood to glove side.
“He shows it to us at practice when you guys don’t have your cameras on,” Slafkovsky said of Dvorak’s backhand.
The Canadiens killed a penalty in overtime after Slafkovsky was called for holding at 2:35.
“I made a mistake and they saved me,” Slafkovsky said. “Obviously I wasn’t breathing in the box and they did a great job, and I had to make sure that I come to each one of them and thank them for saving me because you don’t want to lose like that, a stupid penalty in overtime. They did a great job and I just had to tell them how good they were out there.”
Sam Malinski put Colorado up 1-0 at 7:35 of the first period. He one-timed a slap shot to the stick side from above the right face-off circle off a back pass from Joel Kiviranta.
Ryan Lindgren made it 2-0 at 10:09 with a wrist shot to the glove side from the inside edge of the left circle off a backhand feed from Nelson.
Martin Necas pushed it to 3-0 with a power-play goal at 5:24 of the second period. He was on the left post to slam in a feed across the goalmouth by Drouin.