Kenny Cooper earlier scored his ninth season goal and put the visiting Dallas squad up 1-0 when he gathered a ball in the box and roofed keeper Brad Guzan with a finessed outside-the-foot shot in the 55th minute.
FC Dallas (14-8-4) extended its lead over second-place Houston to 12 points and will clinch a playoff spot with a win Wednesday if the last-place Los Angeles Galaxy loses its match Sunday.
Chivas (8-7-11) moved into a tie for points with the Colorado Rapids in the three spot, each with 35. The second-place Houston Dynamo squad sits only one point ahead in the Western Conference.
Saturday's match marked the third of four meetings between FC and Chivas this season. The clubs split their first two meetings, each picking up a win on their home turf.
They will conclude the season series Sept. 13 in San Francisco.