Brown's goal was the quickest in Rapids history, and he added another in the 31st minute as the home side built a 4-0 halftime lead before coasting home with three points to move to within one point of third-place Portland.
The result snaps Seattle's seven-match unbeaten streak and drops the club one point back of Real Salt Lake at the top of the Western Conference.
The fast start came right from the kick off as Gabriel Torres fed a pass into the area for Brown to slot inside the far post.
Vicente Sanchez was the architect of the second goal in the 10th minute when his quickly-taken corner kick caught Seattle napping, allowing Dillon Powers to score on a glancing header.
Powers played provider on the third goal in the 31st when he got the ball forward to Brown, who turned past his defender and beat goalkeeper Michael Gspurning.
Another Sanchez corner kick a few minutes before halftime led to the fourth goal with Drew Moor getting on the other end to redirect the ball over the line.
Sanchez nearly scored in first-half stoppage time but his free kick struck the crossbar as the Sounders limped into the break.
Colorado eased up a bit after the interval and Eddie Johnson scored in the 63rd for Seattle, while he was denied by the crossbar five minutes later.
Seattle's Zach Scott collected a second yellow card 11 minutes from time, and Gabriel Torres capped a memorable evening for the Rapids with his first MLS goal in stoppage time.
10/06 00:29:20 ET