The home side took the lead in the 20th minute when Zardes collected Marcelo Sarvas's cross from the right on the edge of the box and fired a low effort into the bottom corner via the post.
Los Angeles could have doubled their lead a minute later as Robbie Keane and Robbie Rogers exchanged passes that allowed the striker to cross for Zardes, but he just couldn't get a toe on the ball that would have resulted in a certain goal.
In the second half, Penedo kept his side in the lead with a brilliant reaction save to deny Joao Plata as he hit a first-time shot at goal from close range after latching onto Tony Beltran's cross from the right.
Landon Donovan had a chance to seal his side's win in the 90th minute when he was put through on goal, but he lost his footing at the crucial moment as he tried to round Nick Rimando and the visitors cleared the danger.
The Galaxy were handed a chance to wrap up the game deep in stoppage time when Rimando felled Sarvas in the area and a penalty was awarded. Sarvas took the spot kick himself but saw his effort saved by the Salt Lake keeper, although the home side still saw out the win.