Luongo leaped in front of Cahill to head in a cross from defender Ivan Franjic and 30,000 fans at Melbourne's Rectangular Stadium roared with delight after they were earlier left stunned by Kuwaiti Hussain Fadhel's headed goal after eight minutes.
Cahill, so long Australia's saviour, cancelled out Fadhel's early goal in the 33rd minute after a brilliant jinking run by Luongo, who eluded three opponents near the right corner before crossing low into the path of his team mate.
Earlier, Australia's hopes of a confidence-building start in Group A were torpedoed by some sloppy set-piece defending.
The 30-year-old Fadhel latched onto a neat deflection from team mate Fahed Al Ebrahim after a low corner had whizzed into the heart of the penalty area.
The goal sucked the oxygen from the crowd and a disorganised Australia spent much of the half regaining their composure.
The tournament was earlier launched with an opening ceremony featuring hip-hop music and indigenous dancers.
Sixteen of the continent's top teams will battle over three weeks in front of over half a million spectators, organisers estimate, with a global television audience expected to exceed 700 million viewers.
A simple but colourful ceremony for the biggest soccer tournament in Australia's history featured beach towels and water themes.
South Korea and Oman are the other teams in Group A and will face each other in Canberra on Saturday.
(Editing by John O'Brien)
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