Barcelona superstar Neymar scored in each half as Brazil recovered from conceding an early Marcelo own goal to set up a win before hordes of golden-shirted fans at the 61,600 Corinthians Arena in Sao Paulo.
Chelsea midfielder Oscar put the seal on the win with a late strike from distance to trigger delirium.
The host nation's Group A victory was greeted by an explosion of fireworks across Sao Paulo, a sharp contrast to several hours earlier when riot police fired tear gas and stun grenades to disperse angry protests.
The hosts, chasing a record sixth World Cup, had also enjoyed a degree of good fortune in the first half when Neymar received only a yellow card for elbowing Croatia's playmaker Luka Modric.
Moments later Neymar scored Brazil's equaliser to settle home nerves after Marcelo's 11th-minute own goal.
The match had kicked off after a spine-tingling rendition of Brazil's national anthem with fans -- exhorted to unite behind the team by coach Luiz Felipe Scolari -- roaring their support for the "Selecao."
Brazil captain Thiago Silva epitomised the mood, bellowing a rallying cry to his team-mates as they embarked on their quest to earn first title on home soil.
The victory provided a euphoric counterpoint to scenes earlier in the day when violent protests in Sao Paulo had threatened a stormy start to the month-long football extravaganza.
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