The home side had an excellent chance to take the lead when they won a free kick just outside the area, which was taken by Jose Villarreal.
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Stefan Ishizaki nearly put the Galaxy ahead in the 27th minute when he raided forward from the wing and cut infield to fire a shot at goal which went just over the bar.
The winger caused further problems when he beat his man down the right and then lifted the ball into the middle for the run of Villarreal, but he failed to guide his strike on target.
Ishizaki was having his way with the Fire defence as he carved out another opportunity, this time for Gyasi Zardes as the winger fired a low ball across the face of goal but it was just out of the reach.
In the second half, Ishizaki's efforts were finally rewarded when he picked out Villarreal in the penalty area, and this time the midfielder displayed composure to find the back of the net.
The Galaxy secured their win late in the match as Robbie Keane fired the ball past Johnson into the net from close range to clinch the three points at the StubHub Center.