The two-time World Cup winners ran riot with a 5-0 demolition of their hapless hosts, who did well to reach this stage of qualifying for next year's tournament but were totally outclassed by opponents boasting the formidable attacking pairing of Liverpool's Luis Suarez and Paris St Germain star Edinson Cavani.
Maxi Pereira got the ball rolling with the opener for Oscar Tabarez's men after 22 minutes while Christian Stuani made it 2-0 shortly before the interval. Nicolas Lodeiro made it three with 21 minutes remaining, before Cristian Rodriguez added a fourth and Cavani wrapped up the win with a wickedly-struck free-kick in the second minute of added time.
The return match will be played at Montevideo's Centenario stadium next Wednesday, where on this evidence Tabarez's men should have no problem finishing the job off to join Argentina, Chile, Ecuador, Colombia and hosts Brazil as South America's representatives at next summer's global showpiece.
La Celeste began the match as overwhelming favourites against a Jordan side who exceeded expectations by going further into a World Cup qualification campaign than ever before, ultimately booking their place in the play-offs with a victory on penalties over Uzbekistan in an Asian zone eliminator.
Sixty-four places separate the sides in the world rankings and that gulf in class was painfully evident from the outset as the visitors bossed possession.
Suarez spurned a great chance to open the scoring early on when he fluffed his lines from close range, but the opener was not long in coming as Cavani saw his header saved by Mohammad Shatnawi but the loose ball fell to Pereira who made no mistake.
Three minutes before half-time the lead was doubled, Lodeiro's lofted pass into the area just evading the outstretched boot of a Jordan defender and falling for Stuani, who coolly steered the ball home.
Jordan looked to contain the visitors after the break but their resistance was broken in the 69th minute when Cavani surged through the defence and pulled the ball back from the byline to the edge of the area, where Lodeiro arrived on cue to fire high into the net.
Nine minutes later it was four as Rodriguez was gifted time in the box to pick his spot beyond the goalkeeper after being picked out by Alvaro Pereira from the left.
And with the match in stoppage time the rampant visitors had their fifth, Cavani rewarded for his tireless performance with a wonderful free-kick into the top-right corner, as Uruguay moved to the brink of sealing their place for Brazil - the scene of their second World Cup triumph in 1950.