Ben Simon, who is the coach of Grand Rapids of the American Hockey League, ran the bench while Red Wings assistant Doug Houda handled the meetings between periods.
"We are definitely giving [Simon] the win," Houda said. "This was a tough situation for him to have to come up here and take over on short notice."
Akira Schmid made 25 saves for the Devils (10-14-5), who have lost five straight and nine of their past 10 games (1-8-1).
"We're beating ourselves most of the time," Devils defenseman Damon Severson said. "We play well in stretches and then we start shooting ourselves in the foot. It's not fun right now."
New Jersey played with 17 skaters with forward Jesper Bratt being a late scratch because of a non-COVID illness.
"We knew we were shorthanded tonight, which put us in a tough spot," Devils coach Lindy Ruff said. "We started out the way we wanted to play, but their top guys just had a better game than our top guys."
Larkin gave the Red Wings a 1-0 lead at 15:39 of the first period. Filip Hronek sent a long pass off the back boards, and Larkin got to the puck and shot into an open net after Schmid misjudged the bounce.
Michael McLeod tied it 1-1 at 19:11 when his shot from the high slot fluttered past Greiss.
Larkin made it 2-1 at 11:48 of the second period, beating Schmid from the slot off a pass from Vladislav Namestnikov, and Bertuzzi scored 39 seconds later to push the lead to 3-1.
"This is the same thing that has happened to our club over and over," Ruff said. "We make mistakes that turn into goals against. We're just hurting ourselves too many times with poor puck management."