Brodeur, 37, tied the record shutout total Terry Sawchuk, who played for five teams, accumulated from 1949-70.
Brian Rolston and Travis Zajac knocked in goals in the first period and Niclas Bergfors scored on a second-period power play for the Devils, who have won six of their last seven games.
The Sabres' Ryan Miller made 34 saves.
Theater accidentally screens 'Nymphomaniac' trailer instead of Disney's 'Frozen'
Texas principal bans speaking Spanish, stirs controversy