Erick Torres opened the scoring with his eighth goal of the season in the 56th minute for Chivas, which had gone 0-5-3 since beating the Chicago Fire in its season opener on March 9.
Torres' header beat goalkeeper Clint Irwin after Chivas failed to put a shot on goal in the first half. Chavez, who made two appearances for Colorado last season, broke free on a breakaway to beat Irwin in the 67th minute and again off a cross in the 76th minute.
"I liked that team very much and they always treated me very well," Chavez said. "I am a professional and just do my job."
Deshorn Brown scored in stoppage time for Colorado, only the Rapids' third goal in five games.
The Rapids were without leading scorer Vicente Sanchez, who missed a second straight game because of a sprained left knee.
"We obviously had problems in the back of our defense that we need to address," Colorado Coach Pablo Mastroeni said. "They lulled us to sleep, they waited for their opportunities and took full advantage of them."