Maximiliano Pereira put the visitors ahead midway through the first half, before Cristian Stuani doubled that lead from close range three minutes before the break.
Nicolas Lodeiro, Cristian Rodriguez and Edinson Cavani netted further goals for Oscar Tabarez's men in the second 45 minutes, as Jordan's hopes of reaching their maiden World Cup finals suffered a major setback.
The result brings to an end the hosts' 16-match unbeaten run at home and leaves them with a mountain to climb in the return leg next week.
Tabarez made three changes to the Uruguay side that beat Argentina 3-2 in the final match of the South American qualification process, with goalkeeper Martin Silva’s introduction in place of the injured Fernando Muslera among the alterations.
Jordan, meanwhile, were almost unrecognisable from their last competitive encounter - a goalless draw with Oman - with Adnan Hasan and Odai Alsaify just two of the seven players to come in.
Hasan got the first shot on target for the hosts, but his drilled effort from 20 yards was straight at Silva in the Uruguay goal.
The visitors were slow in settling in at the Amman International Stadium, and struggled to create any meaningful chances in the early stages.
They were almost made to pay after 18 minutes when Alsaify beat his man on the edge of the penalty area and forced Silva to tip around his left post for a corner.
But it was the South Americans who took the lead after 21 minutes through Pereira. Mohamad Shatnawi failed to hold onto an Edinson Cavani header following an excellent cross from the right, and Pereira capitalised by latching onto the rebound to put his side ahead from close range.
And Jordan’s dreams of reaching Brazil 2014 took a further blow in the 42nd minute when Uruguay doubled their advantage. Stuani found himself in acres of space at the far post and slotted under Shatnawi after a delightful chipped cross by Lodeiro.
Ahmad Ibrahim inexplicably guided the ball wide of the target from inside the six-yard box 10 minutes into the second period, wasting a glorious opportunity to give Jordan a fighting chance of getting back into the tie.
Substitute Musab Al Laham was then booked for simulation just seconds after coming on when he threw himself to the ground in a desperate bid for a penalty, before Lodeiro made sure of the victory for Uruguay in the 70th minute.
The Botafogo man fired home from the edge of the penalty area with the Jordan defence in disarray, and Rodriguez completed the rout eight minutes later with a left-footed thunderbolt from 12 yards.
Tabarez's side continued to pile on the pressure late on and Cavani got in on the act with a stunning injury-time free-kick to all but secure Uruguay's place at Brazil 2014.