Johnson broke a scoreless tie in the 15th minute with header off a feed from Jack Jewsbury.
Nagbe added a second goal in the 67th minute for the Timbers, who will take a one-goal advantage into the second leg of the Western Conference total-goal series Thursday in Portland.
The Sounders got on the board in the 90th minute when Osvaldo Alonso blasted home a shot from 12 yards out.
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