The Predators lost their sixth straight game after opening the season with two consecutive victories.
Boston twice overcame a one-goal deficit before Begin beat Nashville goaltender Dan Ellis.
Although he suffered the loss, Ellis had his second straight solid outing after giving up three goals on the only three shots he faced against Dallas last week.
Jerred Smithson and Colin Wilson both scored their first goal of the season for Nashville. Michael Ryder and Patrice Bergeron tallied for the Bruins.
Tim Thomas made 28 saves to get the victory. Thomas has a 3-3 record this month, having given up a total of four goals in the victories and 14 in the losses.