Peverley played nine seasons in the National Hockey League, spending time with Nashville, Atlanta, Boston and Dallas. He finished his career having tallied 241 points (84-157—241), including 20 game-winning goals, in 442 regular-season contests. A member of the 2011 Stanley Cup champion Boston Bruins, Peverley accumulated 21 points (9-12—21) in 59 postseason contests with two trips to the Stanley Cup Final, both with Boston. Prior to breaking into the NHL, Peverley played four seasons of college hockey with St. Lawrence (ECAC), skating in 138 games and registering 117 points (44-73—117) for the Saints.