Brodeur had 25 saves and Rob Niedermayer scored for the Devils.
The difference was Anderson, who came up big against the No. 1 team in the Eastern Conference and a goaltending legend in Brodeur.
"I don't have to shoot on him, but just being on the ice with a Hall of Famer, it's an honor to be playing against him," Anderson said of Brodeur.
Brodeur holds the NHL record for wins and shutouts but was outplayed by Anderson on Saturday. The Avalanche goalie was especially strong in the final minutes when the Devils were on a power play and scrapping for the tying goal.
"They're going to do anything to get that game-tying goal, they're going to throw everything at the net," Anderson said. "Our guys did a great job of letting me see the puck and clearing out the rebounds."
The Devils played most of the game without forward Patrik Elias, who left the game on a stretcher with a shoulder injury after being checked by Colorado defenseman Ryan Wilson. Wilson hit Elias with a high check at the Avalanche blue line with 38 seconds gone in the second period on Saturday.
Elias stayed on the ice for about five minutes before he was secured onto the stretcher. He waved to the crowd as he was taken off the ice.
"I don't know exactly how he is," New Jersey coach Jacques Lemaire said. "I do know he's not ready to play now."
No penalty was called on the hit, but 3:06 later Wilson dropped the gloves with Devils defenseman Mark Fraser.
"It was a clean hit," Wilson said. "I know something's going to happen during the game. Better to get it out of the way early instead of waiting for someone to take a run at me."
The Devils didn't have a problem with Wilson's hit.
"When he was hit, he lifted up his shoulder," Lemaire said of Elias. "I think Patrik was a little careless."
Elias is part of the Czech Republic's team that will compete in the Vancouver Olympics next month.
Even with Elias the Devils fell behind early. Stewart scored his 15th goal of the season 3:17 into the game and Galiardi scored his sixth goal with 1:28 left in the first period to make it 2-0.
"We didn't start the way we wanted," Brodeur said. "You don't want to spot a team like that two goals. That's two games in a row we did that."
New Jersey turned up the pressure in the second period, outshooting the Avalanche 17-11. The Devils had great chances to score when they had back-to-back power plays late in the frame, but Anderson came up with big saves to keep the lead 2-0.
"There's no question he's a calming influence," Avalanche coach Joe Sacco said of Anderson. "There is that factor if you do make a mistake, knowing you have Andy back there it's more comforting."
The Devils finally solved Anderson 1:55 into the third when Niedermayer redirected Jay Pandolfo's centering pass through the goalie's pads for his sixth goal of the year.
New Jersey got a late power play and pulled Brodeur with 1:10 left to get a two-man advantage but still couldn't beat Anderson, who made five saves in the last two minutes.
"We had power play opportunities, an area where we have been struggling," forward Brian Rolston said. "We got great shots at the end and their goalie made some great saves."
Colorado placed D Adam Foote (ankle) on the injured list Friday, retroactive to Jan. 8. ... The Avalanche honored Claude Lemieux before the game as part of their season-long salute to alumni. Lemieux played four-plus seasons in Colorado, helping the Avalanche win the 1996 Stanley Cup. ... Avalanche F Marek Svatos returned to the lineup after missing 12 of the last 13 games with a groin injury. Forward Milan Hejduk (knee) was a late scratch from the lineup.