The hosts had to come from behind after Marcelo scored an unfortunate early own goal, but two strikes from the Barcelona star helped Luiz Felipe Scolari's side to a 3-1 victory in Sao Paulo.
Neymar's second came amid controversy as striker Fred appeared to fall under minimal contact from Croatia defender Dejan Lovren in the penalty area.
Japanese referee Yuichi Nishimura pointed to the spot, allowing the 22-year-old to convert and afterwards Neymar was thrilled to have started the tournament with a positive result.
He told reporters: "I think I am happier than I ever dreamt, to start with a victory in the World Cup such as this.
"The whole team deserve praise for being able to keep calm and turn things around."
Neymar's brace saw him named the official sponsors' man of the match, but Scolari was quick to hail the scorer of Brazil's third goal, Chelsea midfielder Oscar, for an impressive showing in midfield.
"Neymar got man of the match, but if there was a second award it should go to Oscar," Scolari said.
"Our statistics after the game shows he was the one who made the most tackles, and made lots of dribbles and crosses - he was our most creative player on the right.
"He was fantastic and that's the kind of player he is and I have always believed in him. Any doubts came from your side, the media. His level may have dropped but I never lost belief in him."
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