Seattle doubled their advantage when Evans lofted a through-ball over the top of the Dallas defence and Johnson latched onto to it, and was left with a simple finish.
Martins could have added another just before the break, but his left-footed shot from 20 yards out went just wide of the post.
After half time, Mauro Diaz nearly got a goal back for the visitors as he twisted and turned in the area before firing a low effort at goal that went inches wide of the target.
Johnson should have added a third for his side but the ball was taken off his feet at the last moment as he looked to slot Lamar Neagle's cross into an empty net.
The Sounders did get a third in added time as Neagle was brought down inside the penalty area by David Ferreira and Evans made no mistake from the spot, slotting the ball into the net to seal the three points for Seattle.