A bright start from the visitors was ruined midway through the first half when Galaxy took the lead thanks to an emphatic finish from Keane, who used some space on the edge of the box to leave Raul Fernandez helpless.
The hosts scored a crucial second goal just before the break when an inch-perfect delivery from Juninho was drilled home by Zardes.
Los Angeles missed chances to extend their lead further in the second half, with both Keane and Samuel Rosa missing the target from promising positions.
Dallas were able to set up a dramatic finish by pulling a goal back in the 65th minute when Tesho Akindele slotted the ball past Penedo, despite appearing to be in an offside position when the pass was played by Jair Benitez.
However, Galaxy were able to survive the late pressure which arrived to hold on for the victory.