Shea's fifth goal of the season came when he got his head on a cross from Jair Benitez and popped the ball past Chivas goalkeeper Zach Thornton inside the far post.
Goalkeeper Kevin Hartman helped Dallas (9-2-9) extend its unbeaten streak to 11 games with a pair of key saves, including a stop on a right-footed shot from Dario Delgado.
Chivas fell to 5-11-4 with the loss and remained mired at the bottom of the Western Conference standings with just two wins in its last 13 games.
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