Costa Rica faces Brazil on Friday, and it is likely going to need at least a draw to have any shot of moving on from the group stage.
Sergej Milinkovic-Savic, whose non-selection during qualifying led to Slavo Muslin's sacking as Serbia coach, nearly broke the deadlock on the stroke of half-time, but his overhead kick was well kept out by Real Madrid 'keeper Keylor Navas in the Costa Rica goal.
He has become the third player to score a free-kick in the World Cup thus far, following on from Aleksandr Golovin and Cristiano Ronaldo's excellent efforts. However, back in 2014, Costa Rica managed to top the Group consisting of England, Italy and Uruguay so its highly improbable that the opposing teams will take Costa Rica lightly this year.
Los Ticos should have gone ahead after 12 minutes when Serbia fell asleep at a corner.
Serbia grew into the game and started to dominate possession, with Costa Rica playing in the same style which brought them so much success in 2014, sitting deep and looking to pounce on the counter-attack.
And even the offensive changes, which saw Christian Bolanos, Joel Campbell and Daniel Colindres come on, could not help them get through the Serbian defence which may have looked vulnerable on paper.
Phil Mickelson freestyles hole 13 of US Open Championship
Open". "In preparation for [Sunday's] forecasted dry and windy conditions and to maintain a challenging yet fair U.S. And that was before anyone had teed off on Sunday. "A pity they managed to destroy a attractive golf course ".
The goal also represented a new record in this World Cup.
Campbell was proving a nuisance, and only a last-ditch challenge from Nikola Milenkovic prevented Costa Rica's substitute from getting in on goal. "I practiced set pieces, and this was enough for three points".
Keylor Navas had to come to his side's rescue on more than one occasion, though there was no stopping Kolarov's free-kick.
After a furious start in which Serbia's Aleksandar Mitrovic had a header scooped off the line and Costa Rica's Giancarlo Gonzalez failed to convert two headed chances, the match settled into a more predictable pattern.
Calvo sent a low strike wide as Costa Rica threatened again before Nemanja Matic and Luka Milivojevic combined to find Milinkovic-Savic, whose overhead kick was saved by Navas with the flag up in any case.
Playing his 104th game for Serbia, becoming the nation's most capped player in history overtaking Dejan Stankovic (including those who played for both Yugoslavia and Serbia and Montenegro, the teams recognised by Federation Internationale de Football Association as the official predecessor teams of Serbia), the right-back was a force down his flank giving Francisco Calvo a tough afternoon.