The Paris St Germain striker scored a brilliant free kick and had a hand in two other goals as the South Americans' firepower proved too much for their Asian opponents, ranked 64 places behind them in 70th by FIFA.
"There are countless ways of winning in football. Today we didn't play well but we have very good finishing," Uruguay coach Oscar Tabarez told reporters.
"Generally we play better, it's unusual what we saw of Uruguay (today)."
The teams, who finished fifth in South American and Asian qualifying, will face off again in the second leg on Nov. 20 in Montevideo with Tabarez free to begin experimenting with his squad ahead of the finals in Brazil.
Cavani could well be rested after he inflicted more than enough damage on Wednesday, providing an assist for Maximiliano Pereira's 22nd-minute opener and setting up the third for Nicolas Lodeiro in the 70th.
Cristian Stuani and Cristian Rodriguez also scored before Cavani capped a perfect night for the visitors with a sparkling free kick in stoppage time.
"We lost because of the difference in experience between the two teams. We tried with all the effort we have and we will try again in the second leg," Jordan coach Hossam Hassan told reporters.
Jordan had shocked many by reaching this final stage of qualifying for the first time, but their bid for one more upset on a fairytale run that began with a win over Nepal always looked unlikely, even before they were hit by injuries and suspensions.
The West Asians refused to baulk at the challenge in front of them, though, and came close to an early goal in the 18th minute when Odai Al-Saify's cross shot from the right almost caught out Uruguayan back up goalkeeper Martin Silva.
Jordan's replacement keeper Mohamad Shatnawi, called in for suspended Amer Shafi, did not fair as well as his counterpart, though, and could only palm a 22nd-minute header by Cavani into the path of Pereira who prodded home for the opener.
Stuani had provided the right-wing cross for the opening goal and he was again afforded too much freedom as he sneaked in at the back post behind a lunging Al-Saify to convert Lodeiro's chipped pass to double the lead in the 42nd minute.
The home side began the second period with renewed vigour and should have halved the deficit seven minutes after the break but striker Ahmad Ibrahim missed from close range when it looked easier to score.
The visitors rode out a short, tricky spell before adding a third in the 70th minute when Cavani strode in behind the clumsy Jordanian backline and past Shatnawi before pulling the ball back for Lodeiro to smash home from the edge of the area.
As tired home heads dropped, Uruguay substitute Alvaro Pereira broke down the left before clipping a cross over to an unmarked Rodriguez, who had time to chest down before smashing home a left-foot strike in the 78th minute.
Cavani then completed the rout with a swerving, speeding set-piece worthy of the finals.
"Our players were heroes during the previous qualifying matches but Uruguay have now put a leg in the World Cup finals," Salah Sabra, vice president of the Jordan Football Association, told Reuters.
"We played very good football in the first 20 minutes of the game and we matched the stars of Uruguay and the result would be different if we exploited two chances we created."