Carl Soderberg and Reilly Smith each supplied a goal and two assists as Boston skated to its seventh win in nine games.
Tuukka Rask stopped 30-of-32 shots.
Craig Smith scored twice for the Predators, who fell for the fourth straight time.
Carter Hutton started in goal but was lifted in the first period after yielding two goals on Boston's first four shots.
Marek Mazanec turned aside 25-of-29 shots the rest of the way.