The Red Wings scored all four goals on special teams, two on the power play and two on the penalty kill. The Devils scored twice on the power play.
"You don't want to give up two on the penalty kill, but it helps when you get two on your kills as well," Detroit coach Jeff Blashill said. "I thought we had a good special-teams plan on both ends of the ice, and we did a nice job of executing it."
WATCH: [All Devils vs. Red Wings highlights]
Martin Frk, Michael Rasmussen and Trevor Daley also scored for the Red Wings (4-7-2), who have won three straight games after losing nine of their first 10. Jimmy Howard made 25 saves.
"Our team is really starting to play really well in the offensive zone, and that's a lot more fun and a lot easier for me," Howard said. "You can see our confidence growing, and that's something we need to keep going with a lot of home games coming up."
Marcus Johansson had a goal and an assist, and Travis Zajac and Nico Hischier each had two assists for the Devils (5-4-1), who have lost five of six and are 0-3-0 on the road.
"We've still got 38 more road games to play, so we better figure this out," forward Kyle Palmieri said. "Everyone on the team has to start bringing energy in every building, not just the Prudential Center."
New Jersey goalie Cory Schneider made 27 saves in his first start of the season. He missed the first eight games after offseason hip surgery before relieving Keith Kinkaid in an 8-3 loss to the Tampa Bay Lightning on Tuesday.
"It felt good to be back out there, but there was definitely some rust that I need to knock off," Schneider said. "My rebound control isn't where I need it to be, and I gave up a goal under my arm."