Clinging to a 1-0 lead after two periods, the Stars doubled their lead 1 1/2 minutes into the third when Benn stripped Columbus defenseman Aaron Johnson of the puck in the crease and whipped a shot past goalie Steve Mason.
After Derick Brassard's power play tally pulled Columbus to within 2-1 5 minutes into the frame, Ryder restored the two-goal cushion with a marker 81 seconds later.
The Blue Jackets' Kris Russell notched an unassisted goal with 3 minutes left, but Kari Lehtonen (38 saves) shut the door down the stretch, preserving the Stars' fifth win in six games to start the season.
Mason turned aside 15-of-18 shots for Columbus.
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