Lundqvist was especially busy in the third period, when he turned aside 18 shots en route to a season-high 42 saves for the Eastern Conference-leading Rangers.
New York moved to 8-1-1 over its last 10 games.
Ryan Callahan, Ryan McDonagh and Artem Anisimov found the net for New York.
Boston, meanwhile, lost for the fifth time in eight contests despite 17 saves from Tim Thomas.
Swim Week Miami Beach 2014 [PHOTOS]