With the game tied at 1, Benn tipped John Klingberg's shot from the top of the slot past the Ducks' Ryan Miller for the go-ahead goal with 5:37 remaining.
Miller made 35 saves 16 days after shutting out the Stars with 41 saves in Anaheim. Kari Lehtonen stopped 26 shots for Dallas.
The third-period power plays were the only ones for the Stars in the game. The Ducks had killed all 25 of their opponents' man advantages in the previous nine games. Dallas had been successful on only four of 36 power plays (11 percent) over 13 games.