Anas Bani Yaseen's bullet header midway through the first half gave the unfancied underdogs a hard-earned and entirely deserved victory in the opening fixture of Group B.
Though content to sit back and counter, Vital Borkelmans' men forced Mat Ryan into regular saves and could have had a second to celebrate if not for a fine save from the Brighton and Hove Albion goalkeeper.
Awer Mabil also tested the woodwork late in proceedings, while Jamie Maclaren had a goal ruled out for offside, but concerns over Australia's ability to replace the goals of the retired Tim Cahill are threatening to linger throughout the tournament.
Australia were nervous from the outset and their sloppy start was punished in the 26th minute, centre-back Bani Yaseen rising unchallenged to head in Mousa Suleiman's corner.
The margin was so nearly doubled four minutes later as Mat Ryan acrobatically tipped Baha Abdel-Rahman's free-kick against the crossbar.
Graham Arnold's men created little in the first half outside of an early Mabil chance, although they were unfortunate not to receive a penalty for Feras Shilbaya's apparent handball shortly before the break.
Chris Ikonomidis came on in place of Robbie Kruse soon after the restart and the Perth Glory winger quickly threatened in following up a shot from Tom Rogic, who scooped a better opportunity over the bar inside the final 20 minutes.
But for all their possession and territory, the Socceroos were scarcely a threat outside of a Mabil shot into the upright and a Jamie Maclaren finish that was ruled out for offside.
Ikonomidis and Jackson Irvine did attempt to force in an equaliser in one final stoppage-time push, but Amer Shafi was up to the task with a smart double save for a jubilant Jordan.
What does it mean? Australia's attack must be addressed
A reported groin problem forced Andrew Nabbout out of Australia's expected starting XI and left Arnold able to select just one member – playmaker Rogic – of his preferred front four.
Hibernian striker Maclaren was inserted at the point of attack but, like the much-maligned Kruse, was ineffective, and questions continue to hang over just how the Socceroos will score the goals needed to be a success in the United Arab Emirates
Top marks for Ateyah
Jordan's paucity of possession, just 23 per cent, meant complete concentration was required in defence and the alert Khalil Bani Ateyah set the standard.
The midfielder was industrious and intelligent inside his own half and finished with 12 tackles and four interceptions in an impressive display.
Luongo lacks intensity
Much was said about Bert van Marwijk's decision not to employ Massimo Luongo at the World Cup but, starting alongside captain Mark Milligan, the Asian Cup's reigning Player of the Tournament did little to prove that decision wrong.
Luongo's decision-making in possession always seemed unnecessarily delayed and he was statuesque as Bani Yaseen nodded home the opener.
Jordan will attempt to build on their tilt at topping Group B when they meet Syria on Thursday.
Australia are in action the following the day, a date with Palestine presenting an opportunity to restore order to their campaign.