Rimando got his 111th career clean sheet, putting him a shutout away from tying Kevin Hartman on the league's career list. Rimando had missed the team's last two matches because of a knee injury sustained on international duty.
The Timbers (0-3-4) have yet to win a match this season. Real Salt Lake is 3-0-4.
Last season real Salt Lake defeated Portland 5-2 in the two-leg goal-aggregate Western Conference final. Salt Lake went on to the MLS Cup match, falling in a dramatic shootout to Sporting Kansas City for the league title.
The Timbers have never won at Rio Tinto Stadium.
The two teams were scoreless in a defense-oriented first half. Darlington Nagbe's shot from the middle of the box was tipped over the bar by Rimando in the 19th minute.
Real Salt Lake got a chance in the 34th minute, but Javi Morales' free kick sailed just over the bar. RSL got another in the 40th minute when Grabavoy's header off Luke Mulholland's cross was grabbed by Portland goalkeeper Donovan Ricketts.
Maximiliano Urruti had two opportunities for Portland early in the second half. His first shot was tipped by Rimando in the 58th minute and his second went just right of the post 2 minutes later.
Grabavoy broke open the scoreless match with his left-footed goal in the 78th minute that sailed past a diving Ricketts and into the bottom corner.
Rimando was the difference in the match, making a pair of dramatic saves of hard shots by Portland's Gaston Fernandez in the final minutes.