In the first round, Kovalchuk outlasted Jean-Sebastien Giguere to the right before burying his wrister.
Brodeur then sealed the win as he made a pad save on Peter Meuller's attempt.
Broduer stopped 28 shots for just his second shutout of the season, but 118th of his career as the Devils won for the fifth time in their past six games.
Giguere was credited with his second shutout of the season as he stopped 33 shots through regulation and overtime for the Avalanche, who had a three-game winning streak stopped.
The Devils remain in the sixth spot in the Eastern Conference with 87 points while the Avalanche sit in the eighth spot in the Western Conference with 81 points.