Victories in their two remaining games will put Jordan into the World Cup and their stretch starts at Australia and then Oman next week.
World Cup 2014 qualifying: Jordan coach Adnan Hamad bullish of chances
The 2010 World Cup was notable for the absence of any of Asia's Arab nations. This time around, Oman and Jordan are looking to put things straight and make history at the same time.
Neither country has ever qualified for the World Cup and they are locked in a three-way tussle with Australia for the second automatic qualifying spot from Group B of Asian qualifying for Brazil 2014.
On Tuesday, Jordan face Australia in Melbourne, knowing that victories in their two remaining games will put them into the World Cup.
Coach Adnan Hamad is not playing down the importance of Tuesday's encounter.
"I think it's the biggest match in the history of Jordanian football," he said. "But the players, the fans and also us as a coaching staff have all the intention of getting the best result from this match.
"We came here for a win."
The Australians are in third place in the group, level on seven points with Jordan, but with better goal difference. Both teams are two points behind Oman – who do not play Tuesday – with one match in hand.
There was a minor diplomatic issue ahead of the match when Hamad said he had been detained by authorities at the Melbourne airport for several hours last week to make secondary checks on his visa.
Hamad said he was more concerned, however, about the scheduling of an Australian Rules football match at Docklands Stadium on Sunday, just 48 hours before the World Cup qualifier. That meant his team would not be able to see or train on the surface until last night.
"It should have been organised in a different way," Hamad said.
The Australians are in a similar position to Jordan – if they can win two home matches in eight days against Jordan and Iraq, they should clinch the second direct qualifying spot.
Oman face Jordan away next week in the final round.
Al Ain striker Alex Brosque is fit again for selection for Australia, who could be in a better position after blowing a 1-0 lead in Japan last week, conceding a penalty in the last minute for a handball which was duly converted.
"In football, you should never look back. The only thing you get is a sore neck," coach Holger Osieck told Australian Associated Press on Monday.
"Jordan are no mugs, they are a very good team, I don't think you [media] are giving them enough credit," he said. "They have beaten Japan and Australia at home, they are a team that deserve your respect and they certainly have our respect, and we know if we don't play our best, there is a chance we won't win the game."
In Group A, South Korea, trying to qualify for the World Cup for the eighth consecutive time, host Uzbekistan. The Koreans lead the group and can be all but assured of securing a spot in Brazil with a win over second-place Uzbekistan in Seoul.
Iran, a point back from Korea and Uzbekistan in third, host Lebanon in Tehran in the group's other match.
The final Group A games next Tuesday will see South Korea host Iran and Uzbekistan at home to Qatar.
The top two teams in each group will qualify, with the third-place teams in each group meeting in a play-off for the right to face a South American team for a spot in the draw.
Follow us @SprtNationalUAE