The ball fell in toward the far post, where Bonansea was able to get a piece of it, sending a bouncing header past Australian net-minder Lydia Williams for the decisive score.
Cristiane scored all three goals for Brazil as they spoiled Jamaica's Women's World Cup debut.
Juventus' Bonansea popped up at the back post to head home the victor having already levelled for the dogged Italians, putting the Azzurre second in Group C, level on three points with Brazil after a Cristiane hat-trick inspired them to a 3-0 thumping of Jamaica in Grenoble.
Timed at exactly 94 minutes and 39 seconds, Bonansea's victor was the latest winning goal scored in normal time of any Women's World Cup.
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"We have the potential to get through, we've just made a decision to go the long way, the hard way about it".
The veteran forward's goal in the 64th minute for the hat trick came on a free kick that curled just under the crossbar.
The trio of tallies were the eighth, ninth, and 10th career goals at the World Cup for the 34-year-old, who plays her club soccer with Sao Paolo in Brazil.
Handed a chance to break her World Cup duck, Kerr's initial effort was saved by Laura Giuliani, but she tapped in the rebound to spark Australia's attack.
The Matildas beginning another World Cup campaign with a loss having also fallen to defeat in their previous two opening games at the tournament.