The two teams now play the second leg in Sydney on Tuesday, with Syria's remarkable bid to reach next year's FIFA World Cup finals in Russian Federation still very much alive.
But Syria leveled from the spot on 85 minutes through Omar Al Somah, who threatrically went down after contact from Leckie when dealing with a cross.
After looking second best for the first hour, Syria threw caution to the wind as the match progressed and were rewarded for their industry with a result that will give them confidence ahead of next week's second leg in Sydney.
The Syrians rallied in the second half, with al-Soma and Omar Khribin creating opportunities.
"It's a bit disappointing to concede a goal the way we did from a decision", he said. "I'm not sure what happened with the penalty - maybe it touched his hand?"
That chance seemed to spurn Australia on, as the Socceroos dominated possession and chances - Juric had an open Kruse in the box but missed the target with a low pass, before a 20-yard strike from Mark Milligan forced a diving save from Ibrahim Alma.
Oil steady as talk of new OPEC deal balances United States exports
Although Chechnya has a population of just over one million, Mr Kadyrov is one of Russia's most influential officials. Putin said on Wednesday it was possible to extend an OPEC deal to cap oil output "at least until the end of 2018".
"We'll go home and get them on a good pitch in front of all our fans who I know will come out in great numbers on Tuesday night".
They had to survive some scares along the way as the Socceroos twice hit the post for the visitors.
Australia's Trent Sainsbury, 2nd left, fights for control of the ball with Syria's Omar Alsoma, left, during the 2018 World Cup qualifying football match between Syria and Australia at the Hang Jebat Stadium in Melaka, Malaysia, Thursday, Oct. 5, 2017.
Crowds thronged to Umayyad Square in Damascus to watch the match on a giant TV screen, waving flags and chanting for their team.
Syria had a surprising run in the third round of the AFC qualifiers finishing third in Group A of the competition with 13 points.
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.