Rimando dove to his left to get a hand on Juninho's penalty kick to earn his fourth shutout of the season. It was awarded after Omar Gonzalez was pulled down in penalty area on a free kick.
Real Salt Lake (2-2-5) had its third scoreless draw of the season and has been held goalless in five games. Last Friday, RSL ended their second-longest scoreless streak in club history at 387 minutes in a 1-1 draw with San Jose.
Rimando wasn't tested until he pushed Alan Gordon's header over the crossbar in the 66th minute. He intercepted a cross on a breakaway in the 70th minute.
Los Angeles (3-2-5) extended its undefeated streak to five games, including three consecutive ties.
The Galaxy had the best scoring chance in the first half, but Gyasi Zardes pushed an open header wide in the first minute of stoppage time. RSL had the only shot on target in the opening 45 minutes.
The game was delayed for an hour because of lightning strikes during the national anthem.