Doyle put Colorado in front with a header off the bottom right corner of the post in the 56th minute. The Rapids' previous win came on May 23, when they beat Vancouver 1-0.
Colorado's Vicente Sanchez opened the scoring off a cross from Luis Solignac in the second minute.
Vancouver (10-7-2), which had won three in a row, tied it 18 minutes later when Kekuta Manneh put away a high-arcing cross from Mauro Rosales.
Colorado (3-6-9), which came into the match having scored a league-low 12 goals, posted its first multigoal game since a 4-0 win over FC Dallas on April 20.