Early in the 1981–82 season, Peterson was dealt to the Buffalo Sabres in a monster six-player trade centered around Mike Foligno and Danny Gare. In Buffalo, he would hit his stride as an NHL player as a key component of one of the best checking lines in the league alongside Craig Ramsay and Ric Seiling. In 1982–83, he set career highs of 13 goals and 24 assists for 37 points, while establishing himself as a top-notch penalty killer and face-off specialist.