Johnson assisted on a Frederic Piquionne tally in the 12th minute, putting the Timbers ahead to stay.
Piquionne returned the favor in the 45th minute, finding Johnson with a pass at the top of the box that the Portland midfielder chipped to himself, then settled onto his left foot for a volley past goalkeeper Clinton Irwin.
Portland hasn't lost since its second game of the season -- a March 9 defeat at the hands of Montreal.
The seventh-place Rapids dropped to 5-7-5.
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