Ange Postecoglou's side were the big casualties on another tricky night of qualifying for Asia's elite, with Iran producing a scratchy display before salvaging a 1-1 draw against Oman in Group D, while South Korea only edged Kuwait 1-0 away in Group G.
Four-times Asian champions Japan also encountered some problems against Syria before a second half flurry handed them a 3-0 win in Muscat, while Iraq snatched a 1-1 draw in Vietnam after a 97th-minute penalty by Younis Mahmoud.
There was no hero for the Socceroos in Amman, however, as a thumping penalty by Hasan Abdel Fattah at the start of the second half and a late second from Hamza Al Dardour sent Jordan top of Group B with 10 points from four games. Australia have nine points.
"Once they got a goal up, the game became a little chaotic and we couldn’t get into any flow," Postecoglou told Fox Sports.
"We had a couple of chances but overall we lost control of the game.
"We had to roll our sleeves up and get a result, and we didn’t tonight which is disappointing."
Only the group winners in the five team pools are guaranteed a spot in the next round of Asian qualifying for Russia 2018 and Australia, winners of their first three matches, now have little room for error.
Iran, who played at last year's World Cup in Brazil, also looked in a sticky situation in Group D after Saad Al Mukhaini put Oman ahead following some poor defending from Ehsan Hajisafi.
The Iranians, though, improved after the break and Hajisafi atoned for his earlier error by firing in a cross from the left which Seyed Jalal Hosseini turned in from close range in the 70th minute.
The two sides are level at the top of the pool on eight points from four games, with Guam, who were not playing on Thursday, a further point back in third.
Japan leapfrogged Syria and went top of Group E after Keisuke Honda's 55th-minute penalty was followed by a close-range effort from Shinji Okazaki, while substitute Takashi Usami added a third in the dying minutes.
"We weren't that good in the first half but made adjustments at the break and improved in the second period," Japan boss Vahid Halihodzic was quoted as saying by Kyodo News.
"All credit to the players. It was a beautiful win and a collective effort."
South Korea capped a miserable week for Kuwait, threatened with a FIFA ban for government interference, by grabbing a 1-0 win thanks to Koo Ja-cheol's 12th-minute header to move three points clear of the hosts in the pool.
Former New Zealand boss Rickie Herbert enjoyed a first competitive win as Maldives boss, a 4-3 victory in Bhutan where the hosts fought back from 4-0 down and threatened a draw with three goals in the last five minutes.
(Editing by Nick Said)
