A ball played in from the flank by veteren Olic was given a slight deflection by Hull striker Jelavic before Marcelo was able to position himself, he himself had finished off Croatia's good build up into a goal and the lead.
Brazil were able to get back into the game with Barcelona star Neymar striking from outside the box with the Croatian keeper not being able to reach the shot which came off the post and in.
The second half provided chances to both sides but Brazil were able to take the lead through a controversial decision by the Japanese referee.
Fred was very lightly handled if not at all by Southampton defender Dejan Lovren and went down which seemingly was enough to convince the officiator of the opening game.
Neymar was able to convert the penalty albeit only just with the keeper getting his hands onto it but nonetheless it found the back of the net.
Croatia had to push forward to try and salvage a point in the game but there efforts were not transformed into a goal and Brazil were handed a chance to add a third which was taken smartly by Chelsea superstar Oscar with a precise toe finding the bottom left corner.
The win most certainly puts the home nation in charge of Group A with Croatia being the main competition to take the group if Brazil did not.