After a goalless first half Kolaraov broke the deadlock when he curled in a brilliant free kick beyond Keylor Navas in the 57th minute to give Serbia the lead.
Costa Rica tried to snatch an equaliser towards the end of the game but Serbia held on for all three points.
Kolarov with a beautiful free kick to give Serbia 1-0 win over Costa Rica
Kolarov's match winning free kick was among the trends on Twitter as some compared its quality to that of Cristiano Ronaldo.
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The full back is know to score free kicks and his latest was very much appreciated by Twitter users.
A fan said, "Kolarov's free kick goal is better than Ronaldo. Kolarov had to beat Keylor Navas. Ronaldo just had to beat David De Karius. Difference in levels."
"Ronaldo: I just scored the best free-kick at this World Cup. Kolarov: hold my beer."
Another fan said, "Excellent free kick by Aleksandar Kolarov to give #Serbia the breakthrough against #CostaRica. It takes something special to beat Keylor Navas, and that was an expert left-footed strike. #Golazo"
The former Manchester City left back was hailed for his performance in the game, as fans gushed over the beauty of his strike.
A fan said, "One of the most underrated left-backs in world football with an outstanding free kick. Take a bow Aleksandar Kolarov."
"There is only one word for that goal from Aleksandar Kolarov, and they'd know about this one in Costa Rica: GOLAZO"
Serbia will take on Switzerland in their next fixture while Costa Rica will hope to bounce back against Brazil on Friday, June 22