Dempsey leads MLS with eight goals. He has at least a goal or an assist in each of Seattle's last six games. It is the second time in his career that Dempsey has had a six-game scoring streak in MLS, having done it previously in 2005 while with the New England Revolution.
Obafemi Martins added a 75th-minute goal for Seattle. The Sounders have won three straight to improve to 5-2-1. Dillon Serna scored in the 62nd minute for the Rapids (3-2-2).
Neagle, a Federal Way native, gave the Sounders a 1-0 lead 15 seconds into the only minute of first-half stoppage time, and was his third goal of the year.
Dempsey made it 2-0 at the outset of the 47th minute, running onto a loose ball at the top of 6-yard box that Colorado goalkeeper Clint Irwin had slapped away, but couldn't latch onto.
Then early in the 52nd minute, Chad Marshall headed Gonzalo Pineda's corner kick toward Dempsey, and Dempsey headed it in just over Irwin's reach.
Neagle assisted on the goal by Martins, which was his third goal of the season.
Seattle is now unbeaten in its last four games. The Sounders return to CenturyLink Field on Saturday to face Philadelphia.