Dallas played a man down over the final 10 minutes, but still scored twice to move into a tie with Vancouver for the fifth spot in the Western Conference. The top five from each conference advance to the MLS playoffs.
After opening the season with eight wins in 13 outings, Dallas had gone 0-5-6 before rallying to pull off the win against Chivas.
Bryan de la Fuente scored the Chivas goal in the 43rd minute, although replays indicated he was clearly offside when he took a pass that Marco Delgado chipped over a wall of defenders at the edge of the penalty area.
Blas Perez tied it in the 71st minute, Ferreira tallied in the 86th and Nunez scored in stoppage time.
Chivas has only one win in its last 19 contests and just four for the entire season.
Ukrainian protestors topple Lenin statue [VIDEO]
Wisconsin business offering 'therapeutic cuddling' forced to close