The Stars were trailing 3-2 with time running out in regulation when they forged a tie. Jamie Benn intercepted a clearing attempt by Detroit's Brian Rafalski and whipped a pass to Brendan Morrow, who one-timed the puck past Chris Osgood for his second goal of the game.
Then in overtime, Eriksson broke into the Detroit zone on a three-man rush but kept the puck and snapped it into the net for the game-winner.
Eriksson added a pair of assists, Brad Richards also scored and Andrew Raycroft stopped 28 shots for Dallas, which won on the road for the second night in a row.
Pavel Datsyuk, Patrick Eaves and Johan Franzen found the net for Detroit, which got 28 saves from Osgood.