The Europeans took the lead thanks to a Marcelo own goal, before talented forward Neymar brought the hosts level just before the half-hour mark as the two sides entered the break level.
Yet after sustained pressure by the Croats, Brazil were awarded a dubious penalty after striker Fred fell to ground after contact with defender Dejan Lovren.
Neymar converted from the spot, before a late Oscar strike topped a 3-1 victory for the Selecao.
And although many felt the referee’s decision, swayed by the fanatical home support, was incorrect, head coach Scolari insists his striker was fouled in the box.
“Thousands didn't see the penalty? The referee saw it and he is the one that decides,” Scolari said after the game. “We also think it was a penalty.
"I watched it 10 times and, for me, it was a penalty."
The Selecao boss then heaped praise on Chelsea attacking midfielder Oscar, who’s industrious work from the middle of the park was capped off with a well-deserved goal late-on.
“He (Oscar) is this player we all know, I had no doubts,” said Scoalri. “He is wonderful, excellent.”
Yet Scolari was equally complementary of his opponents, who he thinks will advance through to the last 16.
"If I could bet who will advance in this group, I would bet on Croatia," he said.
Defender David Luiz also praised the European side, and admitted his side will have it tough for the rest of their campaign.
“The score doesn't show how the game was,” said Luiz.
“Croatia are a good, smart team.
“This is the first step. We have six more steps. We know the other games won't be easy."
Brazil next face Mexico on 17 June in Fortaleza.