Eriksson's second goal of the game came with 7:54 remaining during a scramble in front of the net following a Flames turnover and staked the Stars to a 4-2 advantage.
They would need the goal when Alex Tanguay fired in a backhander 3 minutes later to make it close, but Dallas held on down the stretch for its first win since March 7.
Joey MacDonald turned aside 20 shots in the loss.
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