It was Brazil's first own goal in 94 World Cup matches. Neymar became the first player to see a yellow card of the tournament.
The two teams went into the half-time at 1-1. Brazil had 64 per cent possession of the ball till interval as against the opponent's 36 per cent.
Neymar made it 2-1 for Brazil in a penalty at the 70th minute.
Oscar made it 3-1 in the injury time. A great victory for the Brazilians. The team remains unbeaten on its home soil since 1975.
Cameroon and Mexico are the other two teams in the group.
Goals' Information: Brazil 3 (Neymar 29, 71 Penalty, Oscar 90+1) Croatia 1 (Marcelo own-goal 11)
Brazil: 12 Julio Cesar (gk), 2 Dani Alves, 3 T Silva (c), 4 David Luiz, 6 Marcelo, 7 Hulk, 8 Paulinho, 9 Fred, 10 Neymar Jr, 11 Oscar, 17 L Gustavo
Croatia: 1 Pletikosa (gk), 2 Vrsaljko, 4 Perisic, 5 Corluka, 6 Lovren, 7 Rakitic, 9 Jelavic, 10 Modric, 11 Srna (c), 18 Olic, 20 Kovacic