Rick Nash, Derek Stepan and Kevin Hayes scored for the Rangers, who won for the ninth time in 10 games overall and improved to 16-3-2. New York's 34 points are tied with Dallas and Montreal for most in the NHL.
The shutout was the 57th in regular-season play for Lundqvist and his second against Nashville.
Pekka Rinne made 19 saves for the Predators, who fell to 11-6-3 with their third straight shutout loss.
Nashville hasn't scored in a franchise-record 213 minutes, 47 seconds, since Miikka Salmomaki's goal at 6:13 of the second period in a 3-2 win over Anaheim last Tuesday.
