The Stanley Cup champion Bruins have lost two of three to start the season.
Hejduk scored the Avalanche's first goal of the season. They lost 3-0 at home to Detroit in their opener Saturday night.
"We've had two tough challenges to start the season," Colorado center Paul Stastny said. "It's easy to get up for these games, especially playing a team like this -- the defending champs."
The Avalanche were certainly satisfied to have a win this season despite a low-scoring start.
"To have one goal in two games and have one win, I think we'll take it," Hejduk said.
Boston coach Claude Julien hopes his team will now realize what he's been preaching since the preseason.
"You hope that it's one of those games that we were talking about, that teams are going to come in here and they are going to work a lot harder," he said. "We got outhustled by a team that was a lot hungrier then we were."
The Avalanche started fast, controlling play in the opening period and hardly seemed to get outplayed much of the rest of the way.
"I thought we had some good urgency to start the game," Colorado coach Joe Sacco said. "The guys were really ready to play. They responded well. That's a tough team to play against. They're a physical team and they use their size very well."
Varlamov was acquired from Washington for a pair of draft picks during the summer. He had 36 saves in the loss to the Red Wings.
Hejduk collected a loose puck along the boards, cut to the right circle and sent a wrist shot that slipped inside the right post by Tuukka Rask, who appeared to be partially screened on the shot by defenseman Zdeno Chara.
Chara said it hit his shin pad en route to the net.
"I was screened, but I saw the shot going," Rask said. "It hit a shin."
A few minutes later, Varlamov dove across the crease to make a blocker save on Milan Lucic's wrist shot from in close.
Rask stopped 35 shots in his first start of the season. Vezina Trophy winner Tim Thomas played the first two games in goal for Boston after playing the entire postseason.
"For the first game in a long time, I felt pretty good," Rask said.
Rask was tested early and often. The Avalanche had a two-man power play advantage for 27 seconds and kept up the pressure, with Stastny hitting the left post on a backhand bid off a rebound in front.
The Bruins had a pair of good scoring chances, both coming on 2-on-1 breaks in the later half of the second period. On the first bid, Daniel Paille's pass went between the legs of a streaking Chris Kelly near the midway point of the period.
Varlamov made a left-pad stop on Brad Marchand's tip from in close late in the period. Varlamov also made a sparkling glove stop on Marchand's wrist shot from the right circle at the end of a 2-on-1 break while Boston was short-handed early in the game.
The Bruins had a 4-on-2 break early in the third, but Varlamov made a right-pad save on Patrice Bergeron's shot from the slot.
After the Bruins raised their Cup banner on opening night, then had special pregame introductions on Saturday night for the second game, things returned to a regular-season feel in TD Garden.
There was no mention of the Stanley Cup or champions in the introductions. The in-game ads on the Jumbotron, which showed Chara holding the Cup during breaks in the first two games, were replaced by other photos.
The Avalanche were the last team in the Western Conference to score this season. ... Colorado played the first of a season-high five-game road trip and is away for seven of nine. ... Boston plays its first road game of the season on Wednesday night against Carolina and faces the Blackhawks in Chicago on Saturday before returning home to face Carolina on Oct. 18. ... It was the only regular-season meeting between the teams this season.