Wondolowski gave the USA an ideal start, notching his first goal in just the fourth minute, while he wrapped up the victory with another strike on the hour mark.
The two goals ended the 31-year-old striker's eight-match scoring drought at international level.
In South Korea's third and final match of their tour of the USA, the visitors were unable to match their hosts, despite taking more shots at Los Angeles' Stubhub Center.
The result on Saturday saw Hong Myung-Bo's Korean side finish with one win and two defeats from their three games, while they only managed to score one goal.
The Americans were clinical in front of goal at LA Galaxy's home ground, taking three shots for the game, which were all on target, with Wondolowski converting two of those opportunities.
Graham Zusi set up the home side's opener and 15 minutes into the second half, the 27-year-old midfielder from Sporting Kansas City was again the provider when his cross was deflected into Wondolowski's path and the Earthquakes forward slotted the ball into the top corner.
USA head coach Jürgen Klinsmann tasted victory with his team for the first time in three games, after a 0-0 draw with Scotland and 1-0 loss to Austria in friendlies in November.
Hong will head back to South Korea with plenty of questions to ponder after watching his team knock off Costa Rica 1-0 and then lose to Mexico 4-0 in their previous two games on American soil.
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