Although the Galaxy remain third in the division after a 2-1 setback, they have only a one-point cushion over the Seattle Sounders.
And while last year's MLS Cup winners have two games left to play in the regular season, Seattle have four, including a home assignment against the lowly Portland Timbers on Sunday.
Robbie Keane fired Los Angeles ahead in the 18th minute against Salt Lake, connecting perfectly beyond the far post with a cross from the right and drilling a 15-yard volley across goal and into the bottom right corner.
But the team containing David Beckham and Landon Donovan were pegged back seven minutes later by Edgar Espindola who cracked a powerful low shot beyond Josh Saunders. And Saunders was beaten again in the 28th minute when Espindola flashed a header out of his reach for what proved to be the winner.
Second-placed Salt Lake now have a five-point cushion over Los Angeles who, were they to finish fourth, would have to take on the fifth-placed team in a play-off to reach the Conference semi-final stage.
The New York Red Bulls are also proof that big-name players do not necessarily bring results.
New York have Tim Cahill and Thierry Henry in their ranks but it was Dutchman Sherjill MacDonald who shone in their clash with the Chicago Fire.
MacDonald scored both goals in a 2-0 win for Chicago, netting in the 65th and 78th minutes as the Fire jumped to second in the Eastern Conference. New York began the day second but fell to fourth, overtaken by Chicago and DC United who were 1-0 winners at Toronto FC thanks to an 88th-minute goal from substitute Hamdi Salihi.
The Montreal Impact can no longer reach the play-offs following a 1-1 draw at the Houston Dynamo, for whom the result was also a setback.
Will Bruin put Houston ahead after 44 minutes, and Sanna Nyassi netted a 66th-minute leveller.
Houston stay fifth in the Eastern Conference but their two-point cushion over the Columbus Crew is a fragile one, with the Crew able to overtake them with their game in hand should they beat leaders Sporting Kansas City on Sunday.
There are no such concerns for the San Jose Earthquakes, who are certain to finish top of the Western Conference.
They were 4-1 winners away to the Colorado Rapids, with Chris Wondolowski's hat-trick doing much of the damage.
Marvin Chavez put San Jose ahead after two minutes, before Wondolowski took over, netting in the 11th, 51st and 83rd minutes. Andre Akpan scored a 90th-minute reply for Colorado.
Jack McInerney's 73rd-minute goal gave the Philadelphia Union a 1-0 home win over the New England Revolution, who had Benny Feilhaber sent off late on.