The Timbers had lost once and played to a tie three times before Johnson came through with his second and third goals of the season.
Johnson broke the tie in the 55th minute by scoring from in close off a cross from Diego Chara. He then took a through ball from Darlington Nagbe in the 73rd minute and scored from the extreme left side of the box.
Houston had won three of its first four games this season, but had only two shots on target against Portland goalkeeper Donovan Ricketts.
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