Cristiane tucked in her second goal from a tight angle following the restart as Andressa provided the assist again, before she completed her hat-trick with a powerful freekick that rattled the underside of the crossbar and landed in.
Without Marta, Brazil's Cristiane delivered with a hat trick.
The sixth-ranked Matildas struck first on Sam Kerr's 22nd-minute goal.
Bonansea, however, equalised 11 minutes into the second half after a defensive blunder on the edge of the box.
A late barrage from the resurgent Matildas failed to produce a victor and they were made to pay when Bonansea grabbed her second of the day in injury time to seal a famous result for Italy. Australia were strong but we didn't do ourselves justice.More news: Transfer: Ex-Manchester United coach warns Solskjaer not to sign Bale
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Jamaica as of now have a lot of positives to take away from this tournament by basically qualifying yet they will want to put on a show in their history-production appearance. "Our federation is not the best, but we have to look forward and see that we have a great bunch of girls and continue to build on this".
Andressa had a good chance to double Brazil's lead from the penalty spot seven minutes before the interval but goalkeeper Sydney Schneider denied the forward.
Her first came in the 15th minute off a header and opened the scoring in the 3-0 contest.
England kicked off their Women's World Cup campaign with a win, while Brazil hammered Jamaica and Italy stunned Australia. The 34-year old Brazilian overtook Ronaldo, who was 33 years old when he scored a hat-trick for Portugal against Spain in their 3-3 draw in the men's 2018 World Cup in Russian Federation.
Brazil now sits at the top of Group C thanks to the goal differential tiebreak over Italy, who claimed a 2-1 win over Australia on Sunday in dramatic fashion. Jamaica play Italy in Reims on Friday.