Alexandre Texier and Pierre-Luc Dubois scored third-period goals for the Blue Jackets (1-2-0), who were outscored by the Nashville Predators 8-3 in their first two games of the season.
"It was a matter of time before we got a win -- we just haven't been playing our best hockey," Dubois said. "This is good for our confidence."
Bobby Ryan scored two goals, and Thomas Greiss made 26 saves for the Red Wings (1-2-0), who have lost five straight games to the Blue Jackets dating to the 2018-19 season.
"We competed hard today, which we need to do every day, and I thought we played really well in the first half of the game," Detroit coach Jeff Blashill said. "They weren't at their best early on, and I thought they got better and outskated us in the second half of the game. We started turning the puck over too much and that means you are doing a lot of defending."