Looking for her first World Cup goal, Matildas captain Sam Kerr twice got into dangerous positions in the first five minutes but couldn't get a meaningful shot away.
Barbara Bonansea thought she had opened the scoring for Italy in the eighth minute only for the offside flag to be raised and VAR eventually confirming the striker mistimed her run by the narrowest of margins.
Surviving that scare, Australia went up the other end and won a penalty in the 20th minute after Sara Gama was guilty of bringing down Kerr in the box.
Having won the spot-kick, Kerr stepped up to take it and though having her initial effort saved to the left of goal, she was able to calmly slot home the rebound to give the Matildas the lead.
In an end-to-end affair, Australia nearly bagged a second in the 37th minute as Ellie Carpenter picked out Chloe Logarzo in the box, whose header was just parried away for a corner.
After the break, Bonansea wouldn't be denied a second time as she brought Italy level in the 56th minute after a mistake at the back from Australia.
With the momentum, Italy thought they had taken the lead with just over 10 minutes remaining only for the offside flag to this time deny Daniela Sabatino.
As both sides pushed for a late winner, it would be Bonansea that stepped up as she headed home the winner in the 95th minute following a corner.
The Matildas beginning another World Cup campaign with a loss having also fallen to defeat in their previous two opening games at the tournament.