Avalanche forward Mikko Rantanen had a goal and two assists. He leads the NHL in scoring with 29 points (seven goals, 22 assists).
Nathan MacKinnon scored on a 3-on-2 rush to give the Avalanche a 4-3 lead at 9:02 of the third, Tyson Jost made it 5-3 on the power play at 15:39, and Alex Kerfoot scored with 15 seconds left for the 6-3 final score.
"Mikko gave me so much room, it was a great play by him," said MacKinnon, who beat goalie Jaroslav Halak with a shot from the right face-off circle off a pass from Rantanen. "I just got the shot off quick, but that was all Mikko there."
WATCH: [All Bruins vs. Avalanche highlights]
Colorado tied it 3-3 on Matt Calvert's goal at 2:11 of the third.
The Avalanche's top line of Gabriel Landeskog, MacKinnon and Rantanen combined for three goals and three assists. The Bruins' top line of Brad Marchand, Patrice Bergeron and David Pastrnak had a goal and two assists.
"It's tough against that line. We saw a lot of them tonight," MacKinnon said. "I thought we did a pretty good job. We won our matchup, and that was the goal tonight."
Jake DeBrusk scored twice, Pastrnak scored his NHL-leading 17th goal and had an assist, and Halak made 19 saves for the Bruins (10-6-2), who lost for the first time in three games.
Semyon Varlamov made 20 saves for the Avalanche (9-6-3), who have won two straight after a five-game losing streak.
"We made mistakes, and some of those mistakes we could have helped ourselves, and then you need saves in those situations," Boston coach Bruce Cassidy said. "We gave them a lead, and that's when you hope [Halak] comes through for us. He did a pretty good job on one-and-done, but it was just those odd-man rushes against good players that cost us."