Obafemi Martins also scored for the Sounders (4-3-3), who racked up a third straight win after enduring a five-game winless streak.
Johnson' second goal in the 62nd minute game only seconds after Michel had pulled Dallas into a 2-2 tie on an unassisted tally.
Kenny Cooper also netted a second-half goal for FCD (7-2-3), whose nine-game unbeaten run come to an end.
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