Maximiliano Pereira and Cristian Stuani scored first half goals for the visitors to stifle any chance of an upset at the Amman International Stadium between the teams that finished fifth in South American and Asian qualifying.
Jordan improved after the break but striker Ahmad Ibrahim missed a great chance to pull one back in the 52nd minute as Uruguay rode out comfortable winners with Nicolas Lodeiro, Cristian Rodriguez and Edinson Cavani adding further goals.
The second leg takes place in Montevideo next Wednesday with the winners claiming a place at the 2014 finals in Brazil.
Jordan's slim hopes of reaching their first World Cup were hit by injuries and suspensions to key players, with Uruguay's world class talent proving far too strong for the backups.
Goalkeeper Mohamad Shatnawi replaced Jordan's suspended number one Amer Shafi but he could only palm a 22nd minute header by Cavani in front of goal which Pereira prodded home.
Stuani provided the right wing cross for the opener and the wideman scored himself 20 minutes later when he sneaked in behind Odai Al-Saify at the back post to prod home Lodeiro's chipped pass to double the lead.
A spirited but outclassed Jordan enjoyed a good spell at the start of the second period but Lodeiro then added a third in the 70th minute to crush any faint hopes the hosts may have had with Rodriguez smashing home a fourth eight minutes later.
Cavani, who also helped set up Lodeiro's goal, capped a brilliant night for the visitors with a sparkling free-kick in stoppage time to complete the rout.
(Writing by Patrick Johnston; Editing by Ken Ferris)
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