The Devils (8-0-1) are one of two teams in the NHL (Colorado Avalanche, 8-0-2) without a regulation loss at home, and their nine-game run from the start of the season is tied for the second-longest in their history. The franchise record is 10 games (8-0-2) from Oct. 8-Dec. 6, 2016.
The win came after a 2-3-0 road trip that ended with three straight losses.
"It's great winning at home," Devils goalie Jacob Markstrom said. "We've played a lot of road games lately and I think this group needed to come home, play in front of the home fans, play at 'The Rock' and kind of settle a little bit and obviously get away with two points."
Nico Hischier, Timo Meier and Connor Brown each had a goal and assist, and Markstrom made 32 saves, including a few highlight-worthy stops in the third period, for the Devils (14-7-1).
"He's the reason why you get the two points," New Jersey coach Sheldon Keefe said. "We had to scratch and claw for this one, and get some good fortune and great goaltending, but this will serve us going forward."
Alex DeBrincat, James van Riemsdyk and Dylan Larkin scored, and Cam Talbot made 15 saves for the Red Wings (13-9-1), who had won four of six (4-1-1).
"We had a really good chance to win that hockey game," Larkin said. "We pushed and made it 4-3 (in the third period) and pushed hard. We had a lot of looks. We just didn't bury the [tying goal] and get it to overtime. I feel like if we play that period again, we have a better outcome tonight. That was a pretty solid period where we were putting our foot on the gas pedal."
Markstrom stopped J.T. Compher on a breakaway coming out of the penalty box at 3:58 of the first period. Compher had been assessed a minor for boarding Hischier, a hit that temporarily knocked the Devils captain out of the game.
Meier put New Jersey ahead 1-0 at 12:54 by deflecting Stefan Noesen's shot.