By Bren O'Brien
A first-half goal from Mark Bresciano was topped off by second-half efforts from Tim Cahill, Robbie Kruse and captain Lucas Neill, who scored his first international goal in his 91st match.
The win on Tuesday moves Australia into second place in the Group B standings with one-match remaining, against Iraq in Sydney next Tuesday. A win in that match will ensure the Socceroos a spot in the showpiece 32-team tournament in Brazil next June.
The comfortable manner of this win, secured thanks to goals from Bresciano in the 15th minute, Cahill in the 61st, Kruse in 76th and Neill in 85th will give Australia coach Holger Osieck plenty of confidence going into what he hopes will be the final match of the qualifying campaign.
The loss ends Jordan's hopes of qualifying automatically through to the World Cup and the best they can hope for is to earn a playoff spot with a win over Oman in Amman next Tuesday.
It took some time for a meaningful contest to break out, with long-range shots from Mark Milligan and Saeed Murjan eight minutes in the first signs of intent from either side.
The early inroads for Australia were all being made down the right-hand side and Luke Wilkshire and Kruse opened up Jordan's defence on 14 minutes, but Brett Holman, a beneficiary of a cross from Kruse, hit a shot straight at Amer Shafi while Bresciano shot wide with the rebound.
A minute later, a similar piece of interplay between Kruse and Wilkshire found the former Melbourne Victory man with plenty of space and time to pick out Bresciano, and on the second time of asking the Melbourne-born striker buried his chance for his 13th goal in Australia colours.
Bayer Leverkusen-bound Kruse was relishing the return to his former home ground and, after again finding room down the right, he teed up Cahill for a awkward close range shot which sailed just wide.
Jordan's best chances came from long range with Ahmad Hayel's 28th-minute effort fierce enough to concern Mark Schwarzer, who saw the ball whisk over his crossbar.
As the half evolved, the visitors got a better handle on Kruse and as a result Australia's scoring chances were restricted to efforts from set pieces.
Ognenovski failed to head accurately from a corner on 34 minutes, while Bresciano's powerful free-kick was directed straight at Shafia just before half-time.
Jordan looked a lot more composed early in the second half as they patiently sought about breaking down a stubborn Australian defence, particularly down the right where Matt McKay was under siege.
Chances were fleeting and neither Hayel - with a header -or Murjan, with a long-range blast, could find the target just before the hour.
With their own attacking chances drying up, Australia called on local hero Archie Thompson on the hour and the effect was immediate as he played a ball through to Holman, who found Kruse free on the right.
His first-time touch for the cross was sublime as he picked out Cahill on the march at the far post. In customary style, he nodded home to give the home side a stranglehold on the game.
The visiting team lost their impetus from that point and Australia pressed for a third. After a string of half chances, it was hardly surprising that Kruse, Jordan's chief tormentor all night, was able to turn charge into the box and seal the three points 14 minutes from time.
Then it was party time for Neill, who had endured a long international scoring drought but got on the end of a pair of headers from Cahill and substitute Tom Rogic to cap a great night for the home side.
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