Kovalchuk tied the game at one in the opening period with a power play tally, and then sealed the victory with another strike in the game's closing minute.
Goalie Martin Brodeur stopped 31 of 33 shots to earn the victory, his 31st of the season.
The win means New Jersey will enter the postseason as the sixth seed after finishing with 102 points. Fortunately for the Devils, it means a first round matchup with either Florida of Washington, each of whom has far fewer points this season (they will earn the third seed by virtue of their division championship).
The NHL playoffs will begin next week.