The result meant the holders finished second in Group B behind Jordan, whose simultaneous 0-0 draw with Palestine gave the Palestinians hope of qualifying as one of the best third-placed teams.
Syria, vocally backed by thousands of their fans in Al Ain, twice fought back from a goal behind before Rogic slammed home the winner in the third minute of injury time.
Injury-hit Australia, with only six outfield players on the bench, needed just a draw to go through as they kicked off at the same time as Jordan against Palestine.
Syria looked an early threat before Australia started to get a grip on the game and Hibernian striker Jamie Maclaren flashed a header just wide.
There was drama on the half-hour when a Syrian free-kick bounced through a packed penalty area and into the net, but the goal was ruled out for a foul on Mark Milligan.