New Jersey went 0-for-5 on the power play, including a five-minute man-advantage in the first period and a four-minute double-minor in the second period.
"It's frustrating for everyone, for the players out there, players who are not on the ice. We just need to find a way to score," Devils captain Nico Hischier said. "We need to execute better, and sometimes we can take more shots and get more traffic in front of the net."
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.
"It was a lot of special teams out there, and I thought the penalty kill did an unbelievable job," Zibanejad said. "It's a team that can score. I thought we didn't give them much. Maybe in the third a little bit, but overall I thought we did a really good job, and [Shesterkin] played great."
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 best during the first period, when he made 16 saves, including five during a five-minute power play after Rangers forward Matt Rempe was assessed a match penalty for an illegal check to the head on Nathan Bastian at 2:25.
"The 'PK' was confident tonight, and the kills were good," New York coach Peter Laviolette said. "We attacked everything that was a loose puck and really limited the opposition. It was a total group effort and our guys were pretty physical."
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 in the neutral zone, catching the Devils on a bad line change.