Cahill, 37, cancelled out Omar al-Soma's opener in the first half before he leapt to head Australia's precious second goal in the 109th minute for a 2-1 win in the second leg.
After last week's 1-1 draw in Malaysia, Australia won 3-2 on aggregate to reach a final play-off against the fourth- placed team from the CONCACAF federation, currently Panama.
Syria have never reached the World Cup and their hopes suffered a massive blow when Mahmoud al-Mawas was sent off for a second bookable offence in the fourth minute of extra time.
There was huge drama in the dying seconds, when Soma juddered the right post with a vicious free kick. But Australia survived to stay on track for their fourth straight World Cup.