After a 1-0 defeat in Mexico in the first leg, the Sounders fell behind 2-0 in the 23rd minute to a headed goal from Elias Hernandez.
But the match shifted just before halftime when Tigres was reduced to 10 men after a second yellow card was issued to Manuel Viniegra.
The comeback began in the 53rd minute with a wonderful volley from DeAndre Yedlin that beat goalkeeper Jorge Dias de Leon from 25 yards.
And it took only seven minutes for the Sounders to pull level on aggregate as Djimi Traore netted his first Seattle goal in style, hammering a 30-yard volley off the underside of the crossbar that settled over the goal line.
Eddie Johnson was responsible for the winning goal when he tracked down a long ball from Steve Zakuani and beat the goalkeeper at his near post.
Seattle becomes the third team in MLS to reach the semifinals of the competition and the club will face either Santos or the Houston Dynamo in the next round.
03/13 11:27:58 ET