Nichushkin tied it 4-4 with a shot from the right face-off dot off a backhand feed from Martin Necas.
Necas had a goal and three assists, Nathan MacKinnon had a goal and two assists, and Cale Makar had a goal and an assist for Colorado (42-10-9), who have won four in a row and five of six. Mackenzie Blackwood made seven saves on 11 shots before being pulled; Scott Wedgewood made 10 saves in relief.
Necas and Nichushkin scored in the shootout, and Wedgewood stopped Jason Robertson and Matt Duchene.
Wyatt Johnston and Justin Hryckowian each had a goal and an assist and Jamie Benn scored for Dallas (38-14-10). Jake Oettinger made 24 saves.
Makar gave Colorado a 1-0 lead at 3:33 in the first period on the power play with a snap shot from the inside of the right face-off circle that sniped the top corner stick-side.
Miro Heiskanen tied it 1-1 at 7:11 when his point shot deflected off an Avalanche stick in the slot on the power play.
Johnston gave Dallas a 2-1 lead at 10:39 after he circled behind the net and used Colorado forward Zakhar Bardakov as a screen on a snap shot from the slot.
Hryckowian made it 3-1 at 16:07 when he put the puck into an open net from the bottom of the left face-off circle after Blackwood had a miscommunication on moving the puck behind his net.
MacKinnon cut the lead to 3-2 at 19:58 on a one-timer from the bottom of the left face-off circle on the power play.
Benn gave Dallas a 4-2 lead at 1:52 of the second period when he tucked in a behind-the-net pass from Hryckowian.
Necas cut the lead to 4-3 at 8:06 from the top of the right face-off circle.
Dallas forward Roope Hintz left the game late in the second period after a battle along the boards with MacKinnon. He did not put any weight on his left leg as he was helped off the ice by a teammate and a team trainer. It was his first game after missing four due to an illness.
Prior to the game, Dallas general manager Jim Nill said that forward Radek Faksa will be out until near the start of the playoffs after he sustained a lower-body injury while rehabbing an upper-body injury sustained while playing for Czechia in the Olympic Winter Games Milano Cortina 2026.