Neither the Sounders nor FC Dallas could find the back of the net in the return leg at CenturyLink Field as Sigi Schmid's men advanced to the next round on away goals after last week's 1-1 draw on the road.
The Seattle Sounders - Supporters' Shield champions and US Open Cup winners - will renew acquaintances with rivals Los Angeles Galaxy, who only finished three points adrift during the regular season.
Dallas needed at least one goal to make it through the two-legged tie after Osvaldo Alonso's 54th-minute goal cancelled out Michel's 34th-minute penalty at Toyota Stadium.
But it never came, though both teams had their chances throughout the contest.
Fabian Castillo was a threat for Dallas up front, while Seattle pair Clint Dempsey and Obafemi Martins caused plenty of problems in the first half.
The closing moments were tense, with both Dallas and Seattle coming close to breaking the deadlock.
Dempsey attempted a strike at goal six minutes from time, but Dallas goalkeeper Chris Seitz blocked the United States international's attempt with his legs.
And up the other end, Mauro Diaz had the chance to win the tie in injury time, though his low shot was dealt with.
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