Lalas Abubakar scored the lone goal for the Rapids (8-10-8).
The Rapids and Dynamo each had nine total shots, with Colorado registering four shots on goal to three for the Dynamo.
William Yarbrough saved two of the three shots he faced for the Rapids. Steve Clark had three saves for the Dynamo.
Colorado played a man down after Bryan Acosta, who had been shown a yellow card in the 19th minute, was shown a red in the 80th.
Both teams next play Saturday. The Rapids visit the Philadelphia Union and the Dynamo visit Minnesota United.