Bonansea sparked the comeback, getting her first tally 11 minutes into the second stanza.
Kerr threw off her armband in despair on the full-time whistle as the Italian bench exploded onto the pitch.
The defeat represents a huge shock for Australia who must now simply beat Brazil on Thursday to have any chance of progressing, while Italy will nearly surely seal qualification with a victory over minnows Jamaica on the same day. She capitalized on an Australia mistake to set up the equalizer.More news: Samsung Galaxy Note10 Pro conflicting rumors: 45W charging is out
"In the first half, we didn't showcase our qualities".
Italy appeared to take the lead through Daniela Sabatino, who found the net at the second attempt after her initial effort rebounded off the post, but the linesman ruled the striker offside.
Bonansea had a goal disallowed for offside in the eighth minute following a Video Assistant Review.
Bonansea was again the hero after she secured the turnaround win for the Italians.More news: Jets pluck Eagles exec to be new GM
Australia coach Ante Milicic vowed to stay true to the Matildas' style despite the defeat.
There was no place in the team for key midfielder Elise Kellond-Knight, who has battled leg injuries over the past fortnight.
The Matildas will now turn their sights on their next two clashes against Brazil and Jamaica.More news: US Sanctions Iranian Petrochemicals Company Linked to Islamic Revolutionary Guard Corps