The Chelsea playmaker's late goal added to a Neymar double as the hosts recovered from falling 1-0 behind to triumph 3-1 against Croatia in their opening Group A game on Monday.
But the victory was not without incident, Brazil were awarded a controversial penalty when Fred went down easily under a challenge from Dejan Lovren.
That moment proved crucial as Neymar put his side ahead for the first time in the game, with Croatia unfortunate to be defeated having held their own impressively.
Oscar was delighted to come away with the points, although he is aware there is room for improvement versus Mexico on Tuesday.
He said: "The first game is always difficult, especially after conceding an early goal.
"But it was very good. Although we conceded the early goal, we played well and found a response.
"The next game will be hard again. Every game for us is final. We have to fix things and we have to think about the next game."
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