Colorado (8-6-6) won for the first time since June 28 to move into third place in the Western Conference. Chivas USA (6-9-5) was held scoreless for the first time since May 31.
LaBrocca curved in a goal past goalkeeper Dan Kennedy in the 16th minute. Ten minutes later, Moor headed home Dillon Powers' corner kick for a 2-0 lead.
In the second half, Torres dipped in a goal over Kennedy from the corner of the 18-yard box.
The shutout ended Erick Torres' scoring streak at six games — one short of tying the MLS record.