On the winning play, Derek Roy collected a pass from Brenden Dillon and launched a shot at Sergei Bobrovsky, who made the initial stop. But Eriksson was there for the rebound, poking it under the Columbus goalie's right pad for the game-winner.
Roy, Cody Eakin, Antoine Roussel each registered a goal and an assist for Dallas, which won for only the third time in seven contests.
Brenden Morrow also scored and Richard Bachman made 16 stops for the Stars.
Derek Dorsett, Cam Atkinson, Nikita Nikitin and R.J. Umberger all scored for Columbus.
Bobrovsky finished with 34 saves.