Juventus' Bonansea pounced on a terrible first touch from Clare Polkinghorne to race through and level for the Italians 11 minutes after the break after hotshot striker Sam Kerr had rammed home the opener for the Matildas on the rebound from her own 22nd-minute penalty.
Italy returned to the final stage of the World Cup after two decades.
"We created enough chances to win the game, we dominated enough possession but I think at the crucial times we didn't capitalise on that".
Bonansea sparked the comeback, getting her first tally 11 minutes into the second stanza.
In another fixture of Group C, 2007 finalists Brazil enjoyed a comprehensive 3-0 victory over Jamaica, as Cristiane completed a hat trick.
Order was restored in Group C just hours after Italy's upset of Australia. She also scored in the 15th and 50th minutes for the Brazilians, who were playing without star Marta who was ruled out with a thigh injury.
The score stayed level for the majority of the second half before Italy threatened with a free kick in stoppage time.
"In the first half, we didn't showcase our qualities".
However, it was Australia that took the lead when Gama committed a silly foul inside the eighteen-yard box to allow Kerr to slot in her first goal in a World Cup from the rebound after seeing her penalty initially blocked by Giuliani. The 25-year-old was voted England's top women's soccer player of the year by the Football Writer's Association in April after a brilliant campaign with Manchester City. But that was as close as they would come to stealing a point on Sunday.