Portland took a 1-0 lead in the 16th minute when Kris Boyd took advantage of a collision between Chivas goaltender Dan Kennedy and a defender, scoring into an empty net from the middle of the area.
But Moreno got the equalizer for Chivas (2-3-0) in the 48th, heading a pass from Ryan Smith into the lower-left corner from close range.
The Goats went ahead in the 82nd when Smith struck a cross that LaBrocca headed from the box into the bottom left corner.
The Timbers (1-3-1), meanwhile, fell for the second straight time at home.
Celebrity Families of 2014 [PHOTOS]