Salt Lake responded with a chance of their own when they were awarded a free kick on the edge of the area, but Javier Morales's effort went just over the bar.
After the half time, the Timbers came within inches of going ahead as Maximiliano Urruti drove at the Salt Lake defence and fired a shot from the edge of the area, which clattered off the bar and bounced clear.
The roles were reversed minutes later when the home side hit the woodwork after Chris Wingert teed up Morales on the edge of the area, and his low shot beat Donovan Ricketts but struck the base of the post.
However, Salt Lake did take the lead when Grabavoy made a surging run to the edge of the area and then placed a left-footed shot into the bottom corner, past the outstretched hand of Ricketts.
The home side were grateful to keeper Rimando for keeping them in front as he made a great save with his feet to deny Alvas Powell from six yards, after the striker had latched onto a through ball.
Rimando made an even better stop minutes later as he turned Gaston Fernandez's goalbound shot past the post with a diving save to hand his side the three points.