Atkinson scored the tiebreaking goal in the second period, Jenner had a goal and an assist, and Dubinsky had two assists.
WATCH: All Red Wings vs. Blue Jackets highlights
"I'm not just singling out that line or [Bobrovsky]," Columbus coach John Tortorella said. "Our whole team game was better. We had a much greater description as far as how hard you have to play."
Detroit (22-23-10), which has lost three straight, nearly tied the game in the last second but Thomas Vanek's shot hit the crossbar.
Vanek scored, and Petr Mrazek made 37 saves for the Red Wings, who were playing for the first time since the death of owner Mike Ilitch on Friday. A moment of silence was held prior to the game.
"We created enough chances to win, but also we had enough good goaltending to win," Detroit coach Jeff Blashill said. "In the end we didn't come away with any points. That's very disappointing."