Devils coach Lindy Ruff said he thought about calling a timeout after the Rangers' second goal.
"Sometimes when you call a timeout, you're sending a message like, '[Oh man], we're in trouble,' and I didn't think we were really in that much trouble," Ruff said. "All I said on the bench was, 'Let's go get the next goal. If we get the next goal we're back in the game.'"
Hughes gave them a 3-2 lead at 5:44 of the second period by catching Dawson Mercer's high flip pass in stride and sliding the puck through Shesterkin's five-hole.
Michael McLeod made it 4-2 at 9:40. Devils forward Miles Wood's shot deflected off Shesterkin and the crossbar, but Rangers defenseman Zac Jones couldn't clear the puck out of the slot, allowing McLeod to bang it in.
"We like our play right now, but we can't get cocky about it because things can slip," Wood said. "We have to hold each other accountable here."
Vincent Trocheck's power-play goal at 13:18 of the third period got New York to 4-3, but Vanecek made five more saves before Sharangovich made it 5-3 at 19:44 with an empty-net goal.
"I don't think it's a secret that there's some frustration," Trouba said. "That's normal where we're at. We talk about it, stay together as a group. That's what we discussed, things aren't easy right now and we're going to keep fighting and battling until this thing turns for us. There's definitely a sense of urgency."