Brown's initial goal set the record for the quickest in franchise history. Dwayne De Rosario holds the MLS mark with his score 11 seconds in for San Jose against Dallas on Sept. 27, 2003.
"Of course we wanted to start quickly," Brown said. "That's why we wanted to run that play, one we had worked hard often in practice."
On the opening score, Gabriel Torres gained control of the ball along the west sideline and found Brown alone. Brown made several strides before releasing a low driving shot that got past goalkeeper Michael Gspurning's desperation dive.
"I ran hard to a spot," Brown said. "The ball came my way and I just took it."
Dillon Powers, Gabriel Torres and Drew Moor added goals for Colorado (13-9-9). The Rapids, 4-2-0 over their last six games, moved into third place ahead of idle Los Angeles in the Western Conference.
"We had a start teams can only dream of," Colorado coach Oscar Pareja said. "You can work towards a great start, expect them, but you can only dream the way we started."
Eddie Johnson scored for Seattle (15-9-6). The Sounders were 1-0-1 in the first two meetings and dropped to 9-2-2 all-time against Colorado.
"We've got to be ready to play from the beginning," Seattle coach Sigi Schmid said. "You can't give up a goal 13 seconds into a game.
"We can't just walk on the field and assume you are going to win the game," Schmid added.
The Sounders were without leading scorer Obaemi Martins (hip), midfielder Clint Dempsey (hamstring) and defenders Djimi Traore (hamstring) and Leo Gonzalez (hip/groin).
The Rapids kept up the pressure. Vincente Sanchez quickly put a corner kick in play and Powers sent a header into the back of the net in the 10th minute.
Brown scored again in the 31st after Sanchez and Hendry Thomas moved the ball ahead to Brown. Brown beat off pressure from Seattle defender DeAndre Yedlin and beat Gspurning just inside the left post.
Moor made it 4-0 off Sanchez's corner kick in the 41st.
Johnson had Seattle's lone scoring chance when his shot grazed the crossbar in the ninth minute.
The Sounders picked up the pressure after intermission. Colorado goalkeeper Irwin stopped Johnson's header early in the second half.
He couldn't stop Johnson in the 63rd.