The victor faces the fourth-place team from Concacaf in November for a berth at the World Cup.
The Socceroos then opened the scoring five minutes before half time when Mathew Leckie got in behind the Syrian defence, cutting back and firing in a shot-cum-cross with his left foot that was turned in by Robbie Kruse for his first goal for Australia since the 2015 AFC Asian Cup.
Omar Kharbin had a shot blocked by Leckie, before Al Soma headed a good chance over and was then denied an nearly certain goal by Milos Degenek's last-ditch lunge.
SYRIA striker Omar Al Somah converted an 85th-minute penalty to keep the war-torn country's World Cup dream alive yesterday.
As the game headed into the final quarter, Ouday Jaffal had a close-range free kick cleared off the line and Khribin's deflected set piece sailed just wide.
"You expect that from this referee, we've had him before".
But Syria were looking unsafe and Khribin had a shot blocked by Leckie, before Soma headed a good chance over and was then denied an nearly certain goal by Degenek's last-ditch lunge.
It sets up a nerve-wracking second leg in Sydney on Tuesday, with the eventual winners going into another play-off with a CONCACAF federation team for a spot at Russia 2018.
In the dying moments, Trent Sainsbury had a close-range header saved and Australia goalkeeper Mat Ryan clawed away a Moayad Al Ajan shot.