Brad Hawpe and Troy Tulowitzki notched solo home runs for the Rockies, who have won three in a row.
Chachin (3-2) gave up two runs on four hits and struck out five. Manuel Corpus pitched the ninth inning and came away with his fourth save of the season.
Ian Kennedy (3-3) took the loss. He allowed three runs on five hits in five innings. Kennedy struck out two but also gave up four walks.
Conor Jackson and Jason Upton drove in the Arizona runs in the sixth inning. The Diamondbacks were outhit by Colorado 7-5.
Colorado jumped to a 3-0 lead with two runs in the second and another in the third on Tulowitzki's fifth home run of the year.