Trailing 3-2 in the fourth minute of stoppage time, Juan Manuel Martinez equalised with the last kick of the match to earn a share of the spoils in Sandy, Utah.
Joao Plata had reduced the deficit in the 67th minute, just as the Galaxy were cruising away from home at Rio Tinto Stadium.
A Giovani dos Santos brace had the Galaxy leading 3-1 past the hour-mark, after Plata's 53rd-minute penalty cancelled out Emmanuel Boateng's first-half opener.
The draw left second-placed RSL and Galaxy level on 48 points in the Western Conference after 28 matches.
Kaka scored twice as Orlando City crushed 10-man Montreal Impact 4-1.
Chelsea icon Didier Drogba gave the Impact a second-minute lead, only for Brek Shea to hit back for Orlando two minutes later.
It was one-way traffic from that point, with Kaka putting Orlando ahead in the 36th minute before the Brazilian star completed his brace via the penalty spot nine minutes into the second half, after Montreal goalkeeper Evan Bush was sent off.
Drogba then saw his penalty saved with 20 minutes remaining and Carlos Rivas sealed Orlando's victory seven minutes later.
With the win, Orlando climbed into the sixth and final play-off spot in the Eastern Conference, three points behind the Impact.
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