The 22-year-old Jamaican rookie's tally was second-fastest goal in MLS history and set the tone for the Rapids (13-9-9), who used the key victory to grab sole possession of fourth place in the Western Conference.
Brown struck again in the 31st minute while Dillon Powers and Drew Moor each added a first-half goal and Gabriel Torres scored in stoppage time for Colorado.
Eddie Johnson got the only goal for the Sounders (15-9-6), whose seven-game unbeaten streak was snapped.
UPI Sports Results for September 20, 2014
UPI Sports Results for September 19, 2014