Serbia beat Costa Rica 1-0 after a wonderful free-kick from Alexander Kolarov just before the hour-mark.
He produced a curling effort to break the deadlock against stubborn opponents.
Serbia had dominated after a bright start from Costa Rica, which saw Gonzalez put over a free header at the back post.
Milinkovic-Savic went close for the Europeans with an audacious overhead kick, but the match was all-square at the break.
But after captain Kolarov scored his free-kick, Costa Rica's best chance fell to Joel Campbell, who delayed for too long after appearing to be through on goal.
Five things we learnt from the Costa Rica-Serbia match
Costa Rica are very attacking: Throughout the game Costa Rica focused on attacking. When they conceded it meant that they had to attack more but from the start they looked to get forward.
Serbia focus on long balls: Serbia used their height and strength well today as they played in a number of high balls, from which they created a number of their chances. This worked well against Costa Rica and it is something their next opponents will have to be wary of.
Costa Rica have all their men in front of ball when defending: When it came to defending Costa Rica had all 11 men in front of the ball. This worked well for the first half. However, when frustration kicked in and they gave away a free kick it did not help them as they conceded an incredible goal. This system was in place until Joel Campbell came on and they were forced to play more attacking football.
Serbia keep applying pressure: Even though they were 1-0 up Serbia never sat back. Throughout both halves they focused on committing men forward and putting crosses into the box.
That free kick: Serbia scored an incredible free kick that sealed them the win over Costa Rica. While some say it resembled the one Ronaldo scored for Portugal, Kolarov’s free kick was placed perfectly to the goalkeeper's left and was an early contender for goal of the tournament.