Tyler Toffoli scored two goals, Dion Phaneuf and Adrian Kempe scored, and Anze Kopitar had three assists for the Kings (22-27-4), who won consecutive games for the first time since winning four straight Dec. 18-27. Jack Campbell made 29 saves.
It was Kovalchuk's first game in New Jersey since returning to the NHL. He played four seasons for the Devils and helped them reach the Stanley Cup Final in 2012. He retired from the NHL on July 11, 2013, and after five seasons with SKA St. Petersburg in the Kontinental Hockey League, signed a three-year, $18.75 million contract with the Kings on July 1.
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The 35-year-old was booed each time he touched the puck. He scored on his only shot of the game 17:36 into the third period to give the Kings a 5-1 lead.
"[The reception] isn't something you're expecting, but that's OK," Kovalchuk said. "You know that's their emotions and that's how they react. I was happy when I scored; that's always the best answer."
Kovalchuk has five points (three goals, two assists) in his past five games.
"There are only two guys left (Andy Greene, Travis Zajac) who I played with on the Devils," Kovalchuk said. "The young guys have come in, like [Nico] Hischier; they're a skilled group. This is not their year, but they have a bright future."
Pavel Zacha scored, and Keith Kinkaid made 20 saves for the Devils (20-25-7), who have lost five of their past seven games.
Toffoli scored a power-play goal 32 seconds into the third off a one-timer from the high slot to make it 2-1, and an even-strength goal 35 seconds later off a pass from Michael Amadio for a 3-1 lead.