"Kovy goes in there and gets that first goal, it's kind of a luxury," Brodeur said. "Then it's in my hands after that. It gives us a really good chance to win."
New Jersey picked up its league-leading 11th shootout win, ending Colorado's three-game winning streak. The Avalanche are 9-2 in shootouts.
It was a night that belonged to the goaltenders. Brodeur, the league's all-time victories leader, picked up his 118th shutout. Jean-Sebastien Giguere got his 36th at the other end.
Brodeur made 28 stops through overtime, while Giguere had 33 saves for Colorado.
The Devils, 5-1 in their last six games, bounced back from a 3-0 loss in Philadelphia on Tuesday. Thanks to Brodeur, they managed a win despite being shut out again.
"We found a way to get a win," said Devils coach Peter DeBoer. "I don't compare this to the Philly game. We created opportunities to score tonight. They just didn't go in."
The Devils squared the season series at 1-1 in the teams' second and final meeting, avenging one of the worst losses of the year, 6-1 in Denver in November.
"We're a different team now than when we played them the first time," Brodeur said. "It's always in the back of your mind when you killed in a game like that. It was nice to come back and win against a good team. We had to play pretty good and Giguere had to make a lot of good saves, especially in the third."
The Avalanche picked up a valuable point in their battle to hold a playoff spot in the Western Conference. They started the night in eighth place, only two points ahead of San Jose, Calgary and Los Angeles. Colorado has won five of its last seven.
Colorado outshot New Jersey 8-5 in the scoreless first period as the Avalanche showed good zip despite needing a shootout to pull out a 5-4 win in Buffalo the night before.
"Marty played a good game and made some key saves tonight," Giguere said. "I thought we did a good job of putting pucks on net and making it hard on him. It was difficult to play back-to-back games."
Jay McClement had Colorado's best chance about 5 minutes in, only to be denied by Brodeur's sharp glove save.
The opportunities were even in the second period as the scoreless deadlock continued. The Devils held a 12-11 edge in shots and both teams missed out on close-in opportunities. Brodeur made a pad stop on Hejduk, and at the other end Jacob Josefson could not steer a wraparound try past Giguere.