The San Jose Earthquakes striker continued his strong run of form with the national team with his eighth goal in nine USA matches.
The U.S. got off to a quick start and was ahead inside four minutes. Graham Zusi was left open to cross the ball in from the right, and Brad Davis got onto the end of it at the back post with a sliding volley. His shot was saved right to Wondolowski, who was in the right place to head into an open net from right on the doorstep.
The Koreans could have equalized just moments later off a corner kick, as a near-post ball was flicked backwards by Matt Besler and just kept out by Nick Rimando, with replays showing that ball may have crossed the goal line.
The visitors had another chance 10 minutes later as a giveaway by the U.S. allowed Lee Keun-Ho to drive into the box, but his shot from close range flew over the bar.
Korea had the better of play for the majority of the half, as the U.S. struggled to maintain possession through the midfield, but the visitors were unable to put together any gilt-edge chances to trouble Rimando in goal.
The U.S. started the second half looking to keep the ball better but again, it was the Koreans who carved out the best early chances, as Shin-Wook Kim won a header that Rimando saved easily.
With 15 minutes gone in the half, though, Wondolowski grabbed his second. A Zusi cross from the right deflected kindly to the Earthquakes striker, who ran onto the loose ball and finished first time from eight yards out.
A noteworthy moment for U.S. fans took place with 15 minutes to play, as DeAndre Yedlin and Luis Gil entered the game at the same time, each earning their first senior cap. Both players were members of the USA's U-20 World Cup squad in 2013.
The Koreans fought to get a foothold back into the match, but despite a number of set piece opportunities, were unable to find a goal, and Jurgen Kinsmann's side saw out a comfortable win.