It was the first win in four tries this season for the Devils, who avoided what would have been their worst start to a season in nine years.
Martin Brodeur extended his NHL career record shutout total to 111 by making 27 saves.
Kovalchuk came to the Devils in a mid-season trade with Atlanta last year and signed a $15-year, $100 million contract prior to the start of the 2010-11 campaign.
He had two assists in New Jersey's season-opening loss to Dallas, but had not produced a point since then until he bested Ryan Miller with New Jersey's 38th shot of the game.
Brodeur, who had nine shutouts last season, earned the 603rd win of his career to extend his league record. He gave up an average of 4.11 goals per game in New Jersey's first three contests.
Buffalo has lost three straight since opening its season with a victory over Ottawa.
Swim Week Miami Beach 2014 [PHOTOS]