Rogic swept home from outside the box in the 93rd minute to cap a man-of-the-match display in a crazy group stage clash in the Khalifa Bin Zayed Stadium in Al Ain.
Australia had twice hit the lead through young guns Awer Mabil and Chris Ikonomidis, before Syrian stars Omar Kharbin and Omar Al-Soma hit back for the Qasioun Eagles.
Mabil's first-half strike - his fourth in seven international appearances - gave Australia the lead before Kharbin equalised two minutes later.
Ikonomidis' first competitive goal for his country early in the second half had Syrian players pleading with Mexican referee Cesar Ramos that the ball hadn't crossed the line.
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