Striker Zigic flicked in a looping cross from Nenad Milijas with the outside of his right boot after seven minutes as Serbia followed up their 1-0 friendly win in Northern Ireland on Saturday with another impressive performance.
"It was an excellent match and the fans made it a very special return for me to Craven Cottage which I remember well from my playing days in England," Serbia coach Radomir Antic told reporters.
"We had a number of experienced players out injured or rested and some of my players have only played a couple of times for Serbia.
"But what was more significant for me, more even than the result, were the qualities the squad have shown me over the last few days. It has been a very good few days for us," said Antic.
Manchester United team mates Nemanja Vidic and Park Ji Sung captained their sides, with Vidic playing superbly at the heart of the Serbia defence and Park orchestrating Korea's moves in midfield.
Serbia's victory represented a first defeat for Korea since they went down 1-0 to Chile in Seoul in January 2008.
"I am disappointed we lost but we played very well against very tough opponents," said coach Huh Jung-moo. "We have learnt a lot from the 0-0 draw with Denmark at the weekend and now today.
"I was very pleased with the way we played and as long as we keep improving between now and the World Cup I will be happy."
