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.
But a largely free-flowing tournament-opener was shrouded in controversy, with Brazil's winner coming courtesy of a dubious penalty when Croatia defender Dejan Lovren was harshly adjudged to have shoved Fred over.
Brazil is chasing a record sixth World Cup
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."
Even after the music stopped, fans and players alike put their hearts and souls into one more verse. 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.