Peverley played hockey in the ECHL for 2 seasons with the South Carolina Stingrays and Reading Royals. He has formerly played for the Nashville Predators for 3 seasons, the Atlanta Thrashers for 3 seasons and the Boston Bruins for 3 seasons. He won the Stanley Cup with the Bruins on June 15, 2011 when the Bruins defeated the Vancouver Canucks in game 7 by a score of 4-0.