Marcus Kruger, Artemi Panarin and Ryan Hartman scored in the second period to give the Blackhawks a 3-0 lead. Kruger scored the third one on a breakaway against Calvin Pickard at 10:57 for his fifth of the season.
The Avalanche answered with shorthanded goals by Duchene and Landeskog 4:15 apart to make it 3-2.
Grigorenko tied the game 3-3 with his 10th goal at 5:46 of the third period off a pass from Duchene.
"That was unbelievable; he kind of just stabbed at it on his backhand," said Duchene, who matched his season high with three points. "He's got a knack for that. That was an unbelievable goal by him, I don't know how he did that."
Duchene, who had gone nine games without a point, converted Matt Nieto's pass on a 2-on-1 at 12:16 for his 18th goal. Landeskog banked his own rebound off Darling at 16:31 for his 17th.
Panarin gave the Blackhawks a 1-0 lead with a power-play goal 28 seconds into the second period. Patrick Kane passed to Panarin, who was wide open at the left circle for a one-timer and his 30th goal.
Hartman made it 2-0 at 4:15. Kruger skated down right wing and fed Hartman, who slipped the puck between Pickard's pads for his 19th goal.
"You want to get up for every game," Hartman said. "Playoffs are two games away and you want to play every game like it's a playoff game just to get our bodies, ourselves amped up for the playoffs. We've got two games left to amp it up."