Alexis Lafreniere scored two goals, Vincent Trocheck had a goal and an assist, and Artemi Panarin had three assists for the Rangers (38-16-3), who have outscored their opponents 39-18 during their winning streak.
Jack Hughes scored, and Nico Daws made 13 saves in his sixth straight start for the Devils (28-24-4), who have lost three of their past four.
New Jersey was 0-for-5 on the power play.
Mika Zibanejad gave the Rangers a 1-0 lead with a power-play goal at 9:14 of the first period. He faked a slap shot in the left circle and tried to send a backdoor pass to Chris Kreider, but the attempt deflected off the stick of Devils forward Dawson Mercer back to Zibanejad, who swatted the puck five-hole on Daws.
Lafreniere made it 2-0 at 17:56 with a wrist shot from the right hash marks following a turnover by Luke Hughes.
Shesterkin was arguably at his during in the first period, when he made 16 saves, including five during a five-minute power play after New York forward Matt Rempe was assessed a match penalty for an illegal check to the head on Nathan Bastian at 2:25.
Kreider pushed it to 3-0 at 9:53 of the second period on a 2-on-1 with Panarin. Shesterkin started the rush by sending an outlet pass to Panarin at center ice to catch the Devils on a bad line change.
Lafreniere made it 4-0 at 19:20 of the second. He took a pass from Trocheck as he split the defense before lifting a forehand over Daws’ glove.
Trocheck extended the lead to 5-0 at 14:29 of the third period, one-timing a pass from Panarin on a 2-on-1.
Hughes scored on a snap shot from the slot at 17:53 for the 5-1 final.
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