With the country gripped by a growing match-fixing scandal, the national team helped local football fans forget troubles on the domestic front with an assured performance.
Park, who is being tipped to move to the English Premier League this summer from relegated French club AS Monaco, headed the opening goal in the 13th minute from a Lee Keun-ho cross.
Serbia, missing a number of its top players including Manchester United captain Nemanja Vidic, hit the woodwork twice in the first half but South Korea always threatened to add to their lead.
The host extended that lead after 54 minutes when Kim scored his first international goal from a Cha Du-ri centering pass.
With less than five minutes remaining, Radosav Petrovic shot into the top corner of the Koreans' net from outside the penalty area but the Koreans hung on for the win.
South Korea next plays Ghana on Tuesday while Serbia travels to Australia.
South Korea has qualified for the last seven World Cups and is preparing for the start of Asian qualification for 2014, which kicks off in September.