The Arab nation will cling on to the belief that miracles do happen.
But Uruguay know that they have one foot firmly in the tournament Finals.
The gap in quality between the two sides had meant that Jordan's hopes rested almost entirely on a good home result to hold on to in the return fixture in Montevideo next week.
Such wishful thinking didn't last very long.
The Uruguayans, semi-finalists in South Africa three years ago, wasted no time in demonstrating their superiority.
Their experience in the World Cup play-offs - this is their fourth consecutive play-off - prepared them mentally for what to expect.
They were sharper, quicker to every ball and defended with an air of confidence expected of overwhelming favourites.
Liverpool's Luis Suarez stretched the home defence to the limit with his trickery, and fired the first warning in the fifth minute when he arrived unmarked in the box to thump a shot over the bar.
Jordan impressed with their pace and commitment but clearly looked a notch below what the visitors were capable of.
The inevitable happened halfway through the first half, when Maxi Pereira slotted in the opening goal after Jordan goalkeeper had kept out Edinson Cavani's header.
The crushing blow came just before the break.
Christian Stuani scored with a side-footed effort to give Uruguay a morale-boosting 2-0 advantage at halftime.
From then on, it was just a formality.
Uruguay didn't disappoint, scoring through Nicolas Lodeiro, Cristian Rodriguez and Edinson Cavani in the second period to complete a comprehensive win. There was no shame in defeat for Jordan, but just a realisation that they are simply not good enough.
Surely now, their fairy tale is over.
And Uruguay look set to go through to another World Cup through the backdoor.
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