Hischier tied it 2-2 on a backhand at 18:24 of the second period, and Palmieri's power-play goal at 11:55 of the third period gave the Devils a 3-2 lead. But Kuhnhackl tied it 3-3 with 5:46 remaining.
"I think we were all finding that energy in the depth of our legs," Lee said. "On these back-to-backs, a lot of it is mental and we talked about that a lot. We're geared up and ready to go, so it's just that mental side of it that you've got to grind through sometimes and we kind of did that a lot tonight."
The Devils defeated the Islanders 2-1 at Nassau Coliseum on Jan. 2.
"We knew after last week they were going to come in ready to go," Palmieri said. "It was a good, tough game. I think in the second period, they had the upper hand. The rest of the game was a good, hard competitive battle."