The only goal of the game was scored by Serbia captain Aleksandar Kolarov in the 56th minute.
Costa Rica and Serbia were drawn in Group along with five-time World Cup winners Brazil and Switzerland.
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Serbia defender and captain Aleksandar Kolarov was named the best player of the game following his side's 1-0 win over Costa Rica in their opening match of the World Cup in Samara.
Serbia will next face Switzerland and Costa Rica will take on Brazil both on Friday.
The 2018 FIFA World Cup kicked off on Thursday and will continue through July 15, with a total of 64 matches set to be played at 12 stadiums across 11 Russian cities.