The Argentine midfielder helped lift the Hoops ahead of the Goats with his excellent service.
Following a scoreless opening period, Dallas scored two quick second-half goals to take control. In the 71st minute, Diaz's free kick was headed down by Hendry Thomas right into the feet of Fabian Castillo, who shot from close range past Dan Kennedy to make it 1-0.
Diaz created Dallas' second as well, picking out Je-Vaughn Watson in the 79th minute with a beautifully weighted pass. Watson pipped ahead of Tony Lochhead to collect and rounded Kennedy before finishing.
Erick Torres pulled one back for the visitors in the 81st minute, his third in three matches. Bofo Bautista played a wide ball from the top of the box to Kristopher Tyrpak, whose near-post cross was turned into goal by Torres.
But Michel restored Dallas' lead with a low, bouncing free kick that deflected under the Chivas wall and skipped inside Kennedy's near post.
Dallas saw Thomas ejected in stoppage time for a harsh challenge on Bofo. Thomas was Dallas' third defensive midfielder to exit the game early after Adam Moffat and Andrew Jacobson left the field with injuries.
Dallas remains unbeaten this season with a 2-0-1 record, while the loss is Chivas USA's first. Its record now stands at 1-1-1.