The Swedish team captain played forward teammate Nathan MacKinnon twice - first to 2-1 with five minutes left of the first period and then to 3-1 with seven minutes left of the second.
Thus, Landeskog has scored six points in the last three matches.
The Colorado star is second in the Swedish points league with 35 points, 3 points behind Nicklas Bäckström, Washington.
After the victory, Landeskog paid tribute to goalkeeper Jonas Johansson, who took 25 of 27 shots.
- He got better the longer the match lasted and it was nice to get a victory for his sake, Landeskog says according to Aftonbladet.
Colorado tops the Western Division two points ahead of the Vegas Golden Knights, who have one game less played.