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.