Cavani's 87th minute clincher from a goalmouth scramble followed fine goals from forwards Luis Suarez and 2009 European Golden Boot winner Diego Forlan, who both ran the disorganised Swiss defence ragged.
Only a solid showing from goalkeepr Marco Woelfli, standing in for injured Diego Benaglio, prevented a Swiss rout and coach Ottmar Hitzfeld was left with more questions than answers.
His side, beset by injury and featuring three debutants, slipped to Switzerland's second consecutive loss since securing a place in the finals in South Africa.
"It's important to throw talent in at the deep end," said Hitzfeld after a game during which he looked increasingly frustrated. "We'll go away and analyse the match."
Uruguay dominated the opening exchanges with the nervous Swiss nearly going a goal down in the second minute as a misjudged backpass from left back Reto Ziegler put through Suarez, who squandered the opportunity by shooting wide.
Switzerland's defence repeatedly left Suarez too much space to show off his skills, leaving Woelfli to deny him through a well anticipated save before another defensive error almost allowed Suarez to put in Forlan.
Switzerland opened the scoring against the run of play as Swiss Super League's top scorer Marco Streller put his case most strongly for a place in Hitzfeld's squad.
Streller took advantage of the absence of usual strike pair Alex Frei and Blaise Nkufo to win a penalty in the 29th minute that was expertly dispatched into the bottom corner by captain Gokhan Inler.
Forlan equalised five minutes later with a volley and Hitzfeld's men were fortunate to end the first half level.
But it was not long in the second half before Suarez latched on to a loose ball from a corner to volley home superbly for Uruguay's second goal, leaving the keeper no chance as the ball sailed into the top corner.
From then on Uruguay seemed content to sit back more and defend Switzerland's largely ineffective attacks, waiting to extend their lead on the break and Cavani eventually supplied the third goal in the 87th minute.
Streller's rival for a place in Switzerland's World Cup strike force, Eren Derdiyok, spurned a golden opportunity in injury time to make his mark.
Switzerland have drawn a tough group at the finals that includes much-fancied European champions Spain, as well as Chile and Honduras.
"Chile are better than Uruguay so we can see what we're up against in the World Cup if we can't beat Uruguay," said Hitzfeld.
