The Sounders were almost at the finish line after a half hour with 10 men before the Crew found a late winner.
Seattle went ahead thanks to Kenny Cooper's first goal of the season in the 23rd minute. Lamar Neagle forced the ball free in midfield and Obafemi Martins played a one-time flick to unleash Cooper down the left wing, and the forward picked his spot to grab his first in a Sounders shirt.
Columbus equalized shortly before the hour mark. Djimi Traore was sent off for kicking at Dominic Oduro when the Crew striker was through on goal, and Federico Higuain converted.
The Crew found their thrilling winner in the 94th minute. Justin Meram, given too much space and time on a short corner with Sounders players packing the goalmouth, picked out his shot from the edge of the penalty area and curled the ball in to give Columbus all three points and keep the Crew perfect in 2014.
Columbus is now 3-0-0, while Seattle is 2-2-0.