The 2-1 extra-time victory came after a 1-1 draw in the first leg, which was played in Malaysia because of the on-going war in Syria.
Syria were reduced to 10 men in the 94th minute and the Socceroos took advantage of the numerical advantage and took the lead in the 109th minute, thanks to the 37-year-old Cahill.
"I don't know why we have to make it so hard - it shouldn't be that difficult for us", Australia coach Ange Postecoglou said.
But a second yellow card to midfielder Mahmoud Almawas in the 95th minute made the challenge even greater for the Syrians.
The move is a huge gamble given the Huddersfield Town man was the standout in last week's opening-leg 1-1 draw, and one that will elicit big questions should Australia fail to progress to a final play-off.
Parity was restored moments later thanks to the early release of Australia's right wing-back Mathew Leckie, who swung in an inch-perfect cross, finding the reliable head of the evergreen Tim Cahill to nod home uncontested.
Syria, which played its home games outside of the country due to the ongoing civil war, finished third in their group.
The midfielder, who plays for the Dhofar Club in Oman, spotted Omar Al Somah's run and threaded a through ball into his path. "Over the last two games - the Thailand game and the other night - he probably could be in double-digit global goals already in his career".
Inside the ground, a group in the Australian section of the ground unfurled a smuggled banner with the words "Free Syria", a revolutionary slogan, which was confiscated by stewards.
As penalties beckoned, Robbie Kruse sent over a cross from the byline and Cahill out-jumped his marker to power a header past the diving Ibrahim Alma.
Australian players and supporters were jubilant.
Tim Cahill and Australia will now take on the fourth place in CONCACAF team in a two-legged playoff to determine who goes to Russian Federation.
The rattling of the woodwork signaled the end for Syria and their against all odds World Cup campaign.