Harris opened the scoring in the 11th minute after sliding to meet a cross from Chris Klute in the box and putting it past a surprised Dan Kennedy.
The Rapids (5-4-4) iced the win in the 78th minute when rookie Deshorn Brown blazed down the right side and fed a cross to Sturgis, who tapped it in for a two-goal advantage.
The win was the third in five games for Colorado, which vaulted over Los Angeles for fourth place in the West.
Last-place Chivas USA fell to 3-7-2.
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