Colombia entered the match at the Estadio Centenario Tuesday needing a victory to secure their place in the World Cup for the first time since 1998, reports Xinhua.
But Cavani struck with a 78th minute header before Stuani prodded in after a clever turn and pass from Gaston Ramirez.
Uruguay are now fifth in the Conmebol standings, level on points with fourth placed Ecuador with just two matches remaining.
In other matches Tuesday, Bolivia drew 1-1 with Ecuador while Venezuela overcame Peru 3-2.
--IANS (Posted on 11-09-2013)