Ivan Demidov and Lane Hutson scored, and Jakub Dobes made 29 saves for the Canadiens (13-8-3), who had won three straight.
"Thought we had a really good start, made a couple mistakes that they made us pay for it," Montreal coach Martin St. Louis said. "Then they get one off the face-off, and then you're kind of chasing the game a little bit, trying to do too much. Our lack of details at that point, I think trying to gain it all back in one play kind of hurt us."
Nelson gave Colorado a 1-0 lead with a wrist shot at 7:32 of the first period. It was his 600th career NHL point.
"I just pride myself on playing both sides and impacting the game in a number of different ways," Nelson said. "Sometimes it might not be the flashiest, but I'm trying to be responsible, and obviously you get a little bit more offense going, it stands out a bit more."
Landeskog extended the lead to 2-0 at 13:25 when Nelson's low shot toward the left post caromed off him and into the net. Montreal challenged the play for goaltender interference, but the call on the ice was upheld after a video review.
Brent Burns pushed it to 3-0 just 50 seconds into the second period with a wrist shot from above the right circle.
"We felt confident coming in," Canadiens forward Josh Anderson said. "Obviously, tough bounce on the second goal. We didn't like the call, but we go down 2-0 and then 3-0. We got to find ways to help out Dobes tonight. I mean, none of those goals are his fault. It's on us as players to be harder to play against."
Nelson made it 4-0 at 3:55, converting at the side of the net off a pass from Necas in front.
"Marty's an unbelievable player, and I feel like you kind of have to be ready a number of different times with him because he's so capable of making spin-o-ramas or a backhand," Nelson said. "He had me fooled. I was in a good spot, and he put it right on my tape for an easy one. I was thinking he was going to maybe rip it backhand, but just a great play by him sucking everybody in. I think the defender kind of thought same thing."