The Red Wings produced two goals in the game's opening 2:40, but could not score again against Sergei Bobrovsky.
Columbus ended a four-game losing streak and handed the Red Wings their fifth straight setback.
The game was marred by an apparent head injury suffered by Columbus center Artem Anisimov. He hit the ice in the second period after tripping over Detroit's Ian White. Detroit's Kyle Quincey also fell and his elbow hit Anisimov's head.
Anisimov was eventually carried from the ice on a stretcher, after which Columbus officials said he was awake and responding. He was taken to a local hospital for evaluation.
The Blue Jackets fought back to tie it 5:03 into the third on a slap shot by Derek Dorsett and Prospal beat Jimmy Howard with a backhander for the game-winner.
Bobrovsky made 28 saves while Howard stopped 21 shots.