Oliver Bjorkstrand and Cam Atkinson each had a goal and an assist, Seth Jones and Zach Werenski each had two assists, and Joonas Korpisalo made 22 saves for Columbus (9-8-4), which has won three straight and is 4-1-1 in its past six games.
"We knew we were playing well, we just had to stay with it," Blue Jackets coach John Tortorella. "All in all, it's a good win in coming back and having a third period like that."
WATCH: [All Red Wings vs. Blue Jackets highlights]
Tyler Bertuzzi scored twice, and Jimmy Howard made 32 saves for Detroit (7-14-3), which is 0-2-2 in its past four games.
"Going into the third, you have a lead, you've got to find ways to win those games," Red Wings coach Jeff Blashill said. "In the NHL, rarely do you lose games when you have the lead like that, and we've got to find a way to win it."
Bjorkstrand tied it 3-3 at 7:40 of the third period, scoring with a slap shot after Howard kicked out a rebound on the power play.