Hosts Australia had the upper hand against China without making the breakthrough, until 35-year-old Cahill pulled out a stunner just after half-time.
The latest wonder-goal by Cahill, whose World Cup volley against the Netherlands was short-listed for goal of the year, was followed by a trademark header by the former Everton man for the 2-0 win.
Australia's victory ended an encouraging tournament for China, who won all three group games for the first time to end their 11-year absence from the knock-out stages.
The Socceroos will now face either Japan or UAE at Newcastle's modest Hunter Stadium, the smallest of the Asian Cup venues, on January 27.
“This is a big win for us, it's something that I knew deep down was going to happen before the game, because I believe in this team," said Cahill. “I had to wait for my chance and I took two of them tonight out of three and I'm pretty happy.”
Son rises to see off Uzbekistan
Earlier in Melbourne, Bayer Leverkusen's Son Heung-Min fought off the lingering effects of a flu bug to strike twice in extra time and see off Uzbekistan — before being stretchered off due to sheer exhaustion.
The man dubbed ‘Sonaldo’ by his team-mates scored with a diving header after 104 minutes and slammed home a second moments before the final whistle, leaving on a stretcher with exhaustion as the Koreans set up a meeting against either Iran or Iraq in the last four.
“There was big pressure on us,” South Korea coach Uli Stielike told reporters after coaxing his team of walking wounded to a fourth straight win. “If we'd lost, we would have been on the plane home and face a lot of criticism.”
Injuries had already ruled out winger Lee Chung-Yong and midfielder Koo Ja-Cheol, while superstar Son has yet to fully regain fitness after being floored by a flu bug earlier in the competition.
“No other team has had to show such mental strength and sacrifice as our boys,” added Stielike. “To lose two of their leaders and still pick them themselves up. I nearly didn't pick Son because of his illness — he's still not 100 per cent.”
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