The Socceroos rebounded from their loss to South Korea in their final group match to beat China on Thursday and advance to the semi-finals, against either Japan or United Arab Emirates.
Cahill's two goals -- the first a bicycle kick and the second from a pinpoint header -- were still the talk of the country on Friday as his team mates gushed about his mesmerizing display.
"You can't say any more. The boy is a freak," said midfielder Mark Milligan.
Veteran midfielder Mark Bresciano was also in awe of his team mate.
"He is a big inspiration not just for the young guys but for all of us," the 34-year-old told reporters.
"He just doesn't stop...he is always capable of getting up and scoring the goals. Got to take your hat off to him."
Defender Trent Sainsbury said Cahill, the oldest in the team at 35, was playing as well as ever.
"Everyone writes him off after he hasn't scored for maybe one game -- and he'll come back and score an overhead like that. It's just incredible," Sainsbury said.
Cahill described his stunning first goal as a "fluke" but said it was his unwavering confidence in his own ability that gave him the belief to try things others wouldn't even consider.
"If you don't have a shot at the title, you don't know if you're going to win," he said. "Nine times out of the 10, I win. That's because I always say I'm fearless when I go onto the pitch.
"It's not cockiness. You have to believe in yourself."
Cahill's second-half brace made up for a patchy performance from the Australians in the first half, where they squandered a series of chances in front of goal.
They also gave up the ball on a handful occasions with captain Mile Jedinak admitting he struggled to produce his best in his first match back from injury.
"It's part and parcel of the game: if you try and force the issue, you're going to make mistakes," Jedinak said.
"What was more important was the way we reacted, even under a little bit of pressure in that first half.
"We took that up a notch in the second half and some individual brilliance from Timmy (won it).
"But overall, the team performance was very, very disciplined -- something I think we've been crying out for."
(Writing by Julian Linden. Editing by Patrick Johnston)
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