Los Ticos might have taken a lead into the break from a functional first half, but Bologna centre-back Giancarlo Gonzalez passed up a standout chance when he was left unmarked before heading over the bar.
In the end the game was settled by a piece of brilliance from Serbian left-back Aleksandar Kolarov, who curled home a stunning free kick in the 56th minute to claim an opening win for Mladen Krstajic's charges.
Relive all of the action with our minute-by-minute updates below.
COSTA RICA STARTING XI: Navas; Acosta, Gonzalez, Duarte, Calvo, Gamboa; Borges, Venegas, Guzman, Ruiz; Urena
SERBIA STARTING XI: Stojkovic; Ivanovic, Milenkovic, Tosic, Kolarov; Matic, Milivojevic; Tadic, Ljajic, Milinkovic-Savic; Mitrovic