Alex Ovechkin scored his 721st NHL goal and had an assist, and Vitek Vanecek made 21 saves for Washington (21-7-4), which has won eight of nine.
Nicholas Merkley, Miles Wood and Jesper Bratt scored, and Mackenzie Blackwood made 18 saves for New Jersey (12-15-4), which had won four of five.
The teams complete the back-to-back set here Friday.
"Well, we've been pretty good at staying focused. Tonight was a little different story," Devils coach Lindy Ruff said. "It just seemed that immediately after [you score] you're looking for momentum, you're looking for a good shift, and we didn't get that, and it ended up in the back of our net."
Bratt tied it 3-3 on a one-timer from the top of the right circle at 11:04 of the third period during a power play.
"I thought we came back and were playing hard, got the power-play goal we needed," Ruff said. "But we didn't execute our breakout, the puck stayed in the zone and they get a lucky bounce [on Kuznetsov's goal]."