Boyd nodded a free kick from Jack Jewsbury toward the bottom left corner of the net, but Gruenebaum laid out to grab the attempt, and the Crew (2-4-2) held on the rest of the way to improve to 0-3-2 in their last five matches.
Boyd also had a golden opportunity for Portland (2-5-2) late in stoppage time from the center of the box but missed after being fed a cross from Jewsbury.
Timbers goalkeeper Troy Perkins came up big in the 65th minute when he leaped to deny a Josh Williams header.
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