Jordan opened the scoring in the Group B contest through a penalty by Hassan Abdul Fattah six minutes into the second half, while Amer Deeb doubled the hosts' lead in the 73rd minute.
Archie Thompson pulled one back for Australia four minutes from full-time, but the visitors could not scramble an equaliser in what time remained.
Defeat leaves Australia winless after three games and on two points, level with Oman and Iraq, who went down to a 1-0 defeat against Japan in the other Group B game.
Japan claimed all the points thanks to Ryoichi Maeda's header after 25 minutes.
The result means Japan, with 10 points, enjoy a commanding lead at the summit. Jordan are in second on four points after their surprise win over Australia.
Korea Republic remain at the summit of Group A despite dropping points in an entertaining 2-2 draw against Uzbekistan in Tashkent.
The hosts went in front in the 14th minute when Ki Sung-yeung headed into his own net but Korea levelled in the 42nd minute when Kwak Tae-hwi nodded home.
Lee Dong-gook put the visitors in front in the 57th minute but two minutes later Uzbekistan secured a share of the spoils when Sanjar Tursunov found the target.
The draw keeps Korea at the top of Group A with seven points from three matches, while Uzbekistan remain bottom of the section on two points.
Lebanon claimed their first ever win over Iran in the day's other Group A contest.
Roda Antar's 27th-minute header secured a 1-0 victory for the hosts in Beirut, as Lebanon moved level on four points with Iran and Qatar.
Tuesday's FIFA World Cup Qualifying (AFC) Results
Uzbekistan 2-2 Korea Republic
Lebanon 1-0 Iran
Japan 1-0 Iraq
Jordan 2-1 Australia