Marcus Foligno's third goal of the year at 15:22 of the second period made interim coach Ted Nolan's return a successful one.
Foligno scored on a backhand shot off a pass from Sabres captain Steve Ott on a 2-on-1 break.
The win was Nolan's first as a Sabres head coach since May 9, 1997, and his first regular-season win behind Buffalo's bench since April 10, 1997.
The Los Angeles Kings beat the New Jersey Devils 2-0 with strikes from Dwight King and Anze Kopitar.
Goaltenders were busy at the Prudential Center, Ben Scrivens making 26 saves for the Kings and Cory Schneider 20 for the Devils.
The Pittsburgh Penguins won 4-1 against the Nashville Predators with scores from Gabriel Bourque, James Neal, Kris Letang and Brandon Sutter. Pascal Dupuis replied for the Penguins.
The Carolina Hurricanes defeated the Anaheim Ducks 3-2 as Riley Nash and Chris Terry scored in the shootout.
Nash scored in the first round of the tiebreaker, but Corey Perry tied it for Anaheim by beating Justin Peters to start the second round. Terry ended the game by beating Viktor Fasth in the third round.
The Columbus Blue Jackets went beyond regulation for the third time in four days and the result was the same.
The Blue Jackets went to a shootout on Friday at home against the Montreal Canadiens and came away with a single point again when David Desharnais scored the lone goal and Peter Budaj stopped all three attempts by Columbus for a 3-2 comeback victory.
The Ottawa Senators ended the Boston Bruins' four-game winning streak with a 4-2 victory at the Canadian Tire Centre.
Jason Spezza, Jared Cowen and Bobby Ryan scored in the third period for the Senators. Chris Neil scored late in the first period for the first of four unanswered goals by Ottawa as the Senators overcame an early 2-0 deficit.
The Washington Capitals were 4-3 winners over Detroit as the Red Wings failed to end their winless streak at the Joe Louis Arena.
Alex Ovechkin scored his 15th goal, and Michael Latta scored his first to erase a two-goal deficit in the third period before Nicklas Backstrom scored the lone goal of a shootout in the third round.
Charlie Coyle's goal with 8:22 remaining in regulation enabled the Minnesota Wild to survive a third-period letdown and escape with a 3-2 victory against the Florida Panthers.
The Winnipeg Jets were 3-2 shootout winners against the Philadelphia Flyers and San Jose won 3-1 against Edmonton.