Kane's point streak (12 goals, 23 assists) is the longest active in the NHL. He passed Stan Mikita's 14-game assist streak (Nov. 26-Dec. 25, 1967) for the longest in Blackhawks history.
"It's nice," Kane said. "I've had some great teammates over the years, and as far as the record goes tonight, a lot of guys burying pucks when I'm passing to them. Pretty cool feeling."
WATCH: [All Devils vs. Blackhawks highlights]
Drake Caggiula, Jonathan Toews and Artem Anisimov scored, and Cam Ward made 41 saves for Chicago (24-25-9), which is 8-1-0 in its past nine games.
Brandon Saad had a goal and an assist to reach 301 NHL points.
"For us, it's playing a consistent hockey game for 60 minutes, regardless of the score or the chances," Saad said. "So for us to fall behind and kind of have a slow start and bounce back, it shows a lot of character in our group."
Damon Severson and Travis Zajac scored, and Cory Schneider made 31 saves for New Jersey (21-28-8), which is 1-4-1 in its past six games and 3-8-1 in its past 12.
Schneider lost his 21st straight regular-season game. He is 0-7-2 in 12 games this season, and 0-17-4 since his last win Dec. 27, 2017.
"I felt really good again," Schneider said. "But again, nothing to show for it in terms of results. Got away from me and us for a couple minutes' stretch there in the third."