Dallas goalkeeper Raul Fernández made seven saves in the goalless draw in Texas on July 4.
Last weekend, the Goats halted their seven-game losing skid with a draw against the New England Revolution. Chivas USA is last in the Western Conference with 13 points from 17 games.
Dan Kennedy blocked a towering Blas Perez in the final few minutes to secure his first shutout of the year. The Goats have conceded a league-high 31 goals in 2013.
FCD is second in the West with 31 points from 18 games.