Martin Brodeur, who has given up an average of 3.02 goals a game this season, surrendered three more against the Sabres but still raised the largest career victory total in NHL history to 628. He is 3-3 this year.
Parise scored shorthanded 2:06 into the game and Kovalchuk added a power-play goal 3:15 later. Kovalchuk returned from a five-game absence brought on by a lower-body injury.
Defenseman Tyler Myers scored his first two goals of the season for the Sabres, who had captured five of their previous six. Myers recorded 21 goals in 162 games during his first two seasons with Buffalo.
Brodeur stopped 29 shots and Jhonas Enroth gave up the five New Jersey goals on 19 shots. Enroth was removed from the game midway through the third period in favor of Drew MacIntyre, who stopped the only two shots he saw.