Ryan O'Reilly and Luke Evangelista each had a goal and an assist, and Roman Josi had two assists for the Predators (1-5-0), who were outscored 23-10 in their first five games. Tommy Novak and Gustav Nyquist also scored.
Jeremy Swayman made 38 saves for the Bruins (3-3-1), who finished 1-1-1 on their three-game road trip.
O'Reilly gave Nashville a 1-0 lead at 17:16 of the first period with a power-play goal on a redirection of a shot by Josi.
Novak extended it to 2-0 at 16:55 of the second period on a rebound of a backhand attempt on net from Evangelista. The goal came just after a four-minute power play had expired for the Predators.
Nyquist pushed it to 4-0 at 12:47 of the third period on a 2-on-1 rush with Filip Forsberg off a pass from O'Reilly.
Evangelista scored an empty-net goal at 13:56 for the 4-0 final.