Gaston Brugman's penalty-kick goal four minutes into first-half extra time gave LA (3-9-3, 12 points) the initial lead, but Real Salt Lake (4-7-4, 16 points) responded with goals from Danny Musovski and Pablo Ruiz in what was looking like a dominant second half for the home team.
Instead, the Galaxy's attack suddenly sparked to life in the 72nd minute. Just 14 minutes after entering the game as a substitute, Rodriguez found room outside the box to convert the equalizer for his first goal with Galaxy.
Los Angeles quickly continued the momentum when Boyd (also a second-half substitute) scored the go-ahead tally in the 74th minute. Calegari had lots of space on the right side to send a cross into the box and past RSL defender Brayan Vera, right to Boyd for his second goal of the season.
It was a stunning offensive surge for the Galaxy, who had scored only 10 goals in their first 14 games of the season. Los Angeles had been shut out in each of its past three games.
The Galaxy had also only scored one goal over their first seven away games (0-5-2) before collecting their first road victory of the season on Wednesday.
The loss ended a three-game (1-0-2) unbeaten streak for Real Salt Lake, who are now 0-2-2 in their last four home games.
Brugman's goal was set up by a video review, as replay determined that RSL's Damir Kreilach committed a hand-ball foul in the box.
Salt Lake responded to the sting of the late concession with an aggressive start to the second half. The pressure paid off with the equalizer in the 51st minute, as Musovski headed in a Jefferson Savarino corner kick.
Ruiz put RSL ahead on another set-piece goal, as the midfielder converted an outstanding free kick in the 67th minute.
--Field Level Media