Australia, who are looking to qualify for their fourth straight World Cup, took the lead early courtesy of Bochum forward Robbie Kruse.
Australia are still in pole position to qualify for the next round - an intercontinental play-off against the fourth-placed CONCACAF nation, which is now the United States.
Al Soma very almost scored from a headed effort that struck Ryan's face en route to the post, one of many near misses for Syria in the second half.
The second leg will be played in Sydney on Tuesday, October 10th, with Wright available for selection once more.
If Syria wins today's match against Australia, they could make history in qualifying World Cup for the first time.
The Syrians came from behind to salvage a draw with the Socceroos, having been awarded a dubious penalty during the second half.
"I think we were a little bit unlucky", Milligan told Fox Sports. "We're very confident. We'll go home and get them on a good pitch in front of our home fans".
Australia coach Ange Postecoglou said he was "bemused" by the late penalty decision, which cancelled out Robbie Kruse's first-half opener and came after Tomi Juric hit the same post twice in quick succession.
From then on, Syria started gaining the momentum and launching counterattacks against a tiring defense.
A speedy burst from Khatib and a header from al-Soma forced a reflex save from Mat Ryan in the 78th and the Australia goalkeeper tipped a hard shot from Moayad Ajan over the bar in injury time to preserve the draw, only moments after Alma made a game-saving stop for Syria at the other end.
The World Cup Qualifiers between Syria and Australia will be live streamed in following channels. Soma also scored the late leveler against Iran that got Syria to this point.
The teams will meet again in Sydney on Tuesday with Australia holding the advantage of an away goal as the Syrians maintained their unbeaten record at their adopted home in the Malaysian city of Malacca.