 Mwaka wakatevera, Riva akaita Serie A yake yekutanga kuCagliari musi wa13 Gunyana, 1964, mukurasikirwa ne2 × 1 neRoma, uye akabatsirawo kirabhu kudzivirira kudzikiswa, achitungamira timu kunzvimbo yechitanhatu yakagadzikana mutafura, achihwina zvibodzwa zvipfumbamwe zvinokurudzira mumitambo makumi matatu nemaviri aine makore makumi maviri. Ikoku kwakateverwa neyegumi nerimwe, yechitanhatu, uye nzvimbo yechipfumbamwe inopedzisa muligi pakati pa1965 na1968, nepo Riva akapedzawo semutambi wepamusoro weligi kekutanga panguva yemwaka wa1966-67 aine zvibodzwa gumi nesere, sezvo kirabhu yakatanga kuvaka chinzvimbo chinogona kuhwina mukombe kutenderedza nyeredzi yavo nyeredzi: Riva akakwezva vatambi venhabvu vanoverengeka kuCagliari, uye timu panguva ino yaive nevatambi vakakosha vakaita saEnrico Albertosi, Roberto Boninsegna, Ricciotti Greatti, Comunardo Niccolai, Mario Martiradonna, Mario Brugnera, Pierluigi Cera, naNené. Riva yakazobatsira Cagliari kusvika kunzvimbo yechipiri muCoppa Italia, kuseri kweRoma, uye muligi, mapoinzi mana kuseri kweFiorentina, mumwaka wa1968-69, kuhwina zita re capocannoniere kechipiri aine zvibodzwa makumi maviri mumitambo makumi maviri nemapfumbamwe; Cagliari anga achitungamira muligi kusvika pazuva rechimakumi maviri nerimwe remutambo, apo kurasikirwa kumba kuJuventus kwakaita kuti timu ibvise kutungamira kwavo. 