With the eight-straight wins setting a new record, Australia now advances to the next stage with 28 goals scored against just two conceded.
The victory in stifling conditions at Jaber Al-Ahmad International Stadium in Kuwait also represents the first time Australia has recorded back-to-back wins over Jordan, who have been knocked out of qualifying.
"I'm extremely proud," said coach Graham Arnold. "I'm so proud because of what these boys have done with winning seven games away from home, eight straight.
"The heat was brutal, 47 degrees and these boys played as though it wasn't hot at all."
"Where are we at [as a team]?" reflected Arnold. "I reckon we're at about 25% of where we'll end up."
It was the Socceroos stiffest test of their qualification campaign but they secured the win through a 77th-minute header from defender Harry Souttar -- his sixth goal in green and gold.
As he has been wont to do through qualifying, Arnold swung a number of changes to the side that last defeated Nepal 3-0; captain Mat Ryan, Trent Sainsbury, Rhyan Grant, Jamie Maclaren and Kenny Dougall all coming into the starting XI.
But it was one of the holdovers that almost gave the Socceroos an early lead when Jackson Irvine advanced into the Jordanian penalty area and hammered a third-minute effort just over the bar.
Seeking to keep their dreams of a maiden World Cup appearance alive, Jordan went close three minutes later when Baha' Abdel-Rahman bent a free-kick just wide of the goal.
Forcing a turnover in the 76th minute, Aziz Behich almost set Australia up to take the lead. He burst forward and delivered a cross that eventually fell for substitute James Holland to hammer a shot that took a deflection and hit the post before being scrambled out for a corner. The Jordanians were unable to prevent near-two meter tall Souttar from heading home the resulting delivery from Martin Boyle.
Jordan's comeback efforts were dealt a hammer blow in the 87th minute when they were reduced to ten men after a frustrated Al-Tamari was shown a red card for striking Behich's face as the latter clashed with Ihsan Haddad over a stiff challenge.
The Socceroos will return to action when the third phase of Asian World Cup Qualifying begins in September.