Both of Holmstrom's goals came on the power play, as the Red Wings went two-for-seven with the man-advantage.
After a scoreless first period that saw the Blue Jackets control the play, Detroit took over the game.
Holmstrom's first goal of the night opened the scoring at 7:06 of the middle frame. Jason Williams one-timed a shot from above the high slot that Holmstrom deflected down at the top of the crease and past Columbus goalie Pascal Leclaire.
Holmstrom's second of the night came 4:52 into the third period. Pavel Datsyuk carried the puck behind the net and sent it out front into the slot, where Holmstrom was open to bang it back at the net and by Leclaire.
Mathieu Schnieder added a goal on a blast from the top of the left circle with 1:47 remaining in the game.
Detroit stopped all seven of Columbus' power play chances.
Leclaire made 37 saves on 41 shots in the Blue Jackets' net.
The Red Wings are back in action on Sunday when they visit the Colorado Avalanche for the first time this season. They earned a 7-3 win over Colorado in Detroit on November 23.
Notes: Henrik Zetterberg missed the game with a hip injury.