Dawson Mercer made it 2-0 at 7:10, collecting the puck off a blocked shot above the left face-off circle and carrying it across before scoring with a far-side shot from the right circle that went in off the inside of Shesterkin's right pad.
"It's got to be sharper in the first when we first take the ice," Laviolette said. "Whether it's effort or whether its execution, it's got to be better right off the bat. It's got to be more consistent through the game. What we're doing isn't good enough."
The Devils killed a penalty on Hamilton at 9:16 by blocking five shots, including four off Zibanejad's stick, in a 30-second span after Pesce's stick broke.
Pesce had three of the blocks. Bratt and Haula had the other two. Markstrom finished it with a save on Kreider on a redirect from the left post.
Bratt had a short-handed breakaway earlier in the kill.
"When it was time to dig in and stand in front of shots and eat a few of those pucks I thought the guys did a tremendous job of that," Devils coach Sheldon Keefe said. "There's a number of guys that took their wounds here tonight. They stood their ground."
Hamilton extended the lead to 3-0 with a 5-on-3 power-play goal at 9:04 of the second period. He scored with a one-timer from the left circle off a pass from Jack Hughes with two seconds left on the 5-on-3.
Jack Hughes scored at 12:38, making it 4-0 with a spinning shot off a rebound of his brother Luke's shot from the left point.
Kreider's power-play goal at 13:29 made it 4-1, but Jack Hughes scored on a 4-on-3 power play at 18:56 to extend New Jersey's lead to 5-1.
"I liked how we went out and when the power play had an opportunity to strike, we did," Keefe said. "Those goals and that ability to extend the lead was really important for us here tonight. It's a team on the other side that we know can score a lot and they had us on our heels a fair bit tonight, but to have that lead takes a little bit of wind out of their sails."
NOTES: Bratt's four points gave him 35 for the season, fifth in the NHL, three shy of League leader Kirill Kaprizov (38). ... Kreider's power-play goal was the 114th of his career and he's now two short of Camille Henry's franchise-record of 116. ... Devils forward Nathan Legare made his NHL debut, skating 11:42 and finishing with two shots on goal and six hits. He was recalled from Utica of the American Hockey League before the game Monday. Legare grew up with Rangers forward Alexis Lafreniere. … Mike Hardman also made his season and Devils debut after being recalled from Utica with Legare. He played 8:24. … Rangers forward Brett Berard (upper body) did not play for the first time in five games since he was recalled from Hartford of the AHL on Nov. 24.