Second-half substitute Montero broke a scoreless tie in the 64th minute shortly after coming into the game, jumping on a layoff from Vancouver defenseman Jeff Parke and putting the ball past goalkeeper Joe Cannon.
The Sounders (11-6-7) doubled the advantage in the 87th minute when Brad Evans slid a pass across the face of the goal to Johnson, who fired it home for his 11th goal of the season.
Vancouver (10-9-7) dropped its second straight.
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