Cavani akahwina paakatanga kuenda kuUruguay achirwa neColombia musi wa6 Kukadzi 2008, uye kubvira ipapo akahwina mitambo 123 uye akahwina zvibodzwa zvepasi rose makumi mashanu neshanu, achingova shure kweanoshanda naye Luis Suárez pakati pevamiriri veUruguay. Akatora chikamu mumakwikwi mapfumbamwe makuru epasi rose: FIFA World Cup muna 2010, 2014 na 2018, Copa América muna 2011, 2015, 2016
, 2019 na2021, uye FIFA Confederations Cup muna 2013. Akawana kamwe chete pa 2010 World Cup kubatsira Uruguay kunzvimbo yechina mumutambo, uye muna 2011 aive chikamu chechikwata cheUruguay chakahwina rekodhi yegumi neshanu Copa América zita. Akapedza semutambi wepamusoro weCONMEBOL 2018 World Cup yekukodzera aine zvibodzwa gumi.