RSL's attacking midfielder continued his fine form with another strong outing against the Rapids.
Morales picked out Plata in the Colorado box 23 minutes into the match and the Ecuadorian finished calmly to put the home side in front.
A penalty just after the break doubled the lead.
Drew Moor was judged to have taken down Devon Sandoval as the two battled in the box. Morales stepped up to calmly finish the spot kick and give the home side a 2-0 advantage.
Moor pulled one back in the 83rd with a header to give his team a lifeline, but RSL manged to hang on for the club's third win in a row and fourth in five games.