Damir Kreilach contributed one goal and one assist as Real Salt Lake (11-10-6, 39 points) won for the fourth time in its past six games and moved into fifth place in the Western Conference, one point ahead of the Galaxy.
Javier "Chicharito" Hernandez scored his 12th goal of the season for the Galaxy (11-11-5, 38 points), who are winless in their past eight matches (0-5-3).
Kreilach set up Julio's decisive goal with a long pass. Once Julio collected the ball, he ripped a left-footed shot from beyond the box past Los Angeles goalkeeper Jonathan Bond. It is Julio's seventh goal of the season.
David Ochoa recorded four saves for Salt Lake, while Bond made two stops for Los Angeles.
The Galaxy held a 20-12 edge in shots and put five on target to RSL's four.
Kreilach scored his 12th goal of the season in the 45th minute on a shot that went off Bond's hands. The ball barely trickled fully across the goal line before Bond slapped it back out.
Chicharito knotted the score in the 76th minute when he received a pass from Efrain Alvarez and turned and sent a left-footed shot into the right corner of the net.
Salt Lake had a chance to regain the lead three minutes later, but Bond made the save on Julio's close-range, right-footed shot.
One minute later, the Galaxy had a solid opportunity, but Dejan Joveljic sent a right-footed blast just over the crossbar.
Joveljic had another chance in the second minute of second-half stoppage time, but his header off a corner kick went just over the goal.
Chicharito also had strong scoring chances in the 16th and 57th minutes.
First, Chicharito saw his right-footed shot saved by Ochoa. In the 57th minute, his close-range right-footer was halted when Ochoa made a fabulous kick save.