Carlos Alvarez, on a fed from Erick Torres, scored for Chivas 5 minutes into the match.
Goats goalie Dan Kennedy kept the Rapids at bay when he stopped a penalty shot by Deshorn Brown in the 28th minute.
Rivero's goal in the 80th minute came on a header into the top left corner off a feed by Chris Klute.
The Rapids are now unbeaten in eight straight games.
Chivas is winless in three consecutive league games since a 1-0 result over Toronto FC on July 17.