Boston (20-3-0) also tied the NHL record for fewest games needed to reach 20 wins with the 1929-30 Bruins (20-3-0) and 2012-13 Chicago Blackhawks (20-0-3).
"We work for each other," Bruins forward David Pastrnak said. "We obviously started [the] season without some key players to the team, and some other guys had to step up, and they did. And sometimes that builds up the confidence [individually], and then obviously that translates to the team."
Pastrnak and Trent Frederic each scored twice for Boston. Charlie McAvoy had two assists, and Linus Ullmark made 24 saves.
"I think we keep playing the right way and we're getting rewarded for it," Bruins coach Jim Montgomery said. "Colorado's very depleted, but still, that's a championship team and they know how to win."
Andrew Cogliano scored, and Pavel Francouz made 35 saves for Colorado (13-8-1). Artturi Lehkonen left the game in the first period with an upper-body injury.
"We're missing good players," Colorado forward Mikko Rantanen said. "One plus one is two, right? If you have good players, like big, important players back, it's different. But like I said, no excuses. Injuries happen in sports, and we're just in a little bit of a slide in that part."
Said Avalanche coach Jared Bednar: "We have to be mentally tough, that's the biggest thing. We still have the ability to win hockey games, although the margin for error is shrinking, and you feel like at times you have to be almost perfect in order to win. We certainly weren't that tonight."