The Blue Jackets are tied with Minnesota for the eighth and final playoff spot in the Western Conference with 53 points, one behind the Detroit Red Wings.
Columbus and Detroit, however, have only one game left to play while Minnesota has two remaining.
Dallas still had a chance at the playoffs when Thursday's games began, but Detroit's win earlier in the evening over Nashville wiped out the last of the Stars' hopes.
The other two Columbus goals both came from Cam Atkinson, who tallied just 19 seconds into the contest and then added an insurance score with 1:40 remaining in the third.
It was the seventh win in eight games for Columbus, which came up with 31 saves from Sergei Bobrovsky.
Kari Lehtonen stopped 32 shots for the Stars.