 Anonzi lAbatino, uye The Golden Boy wenhabvu yeItaly muhupenyu hwake hwese, Rivera aive chigadzirwa chechikoro chevadiki venhabvu yekirabhu yekumusha kwake; akabatana nechikwata chekutanga muna 1958 uye akaita kutanga kwake muSerie A kwechikwata chevakuru cheAlessandria vachipesana neInternazionale musi wa2 Chikumi 1959 aine makore gumi nemashanu chete, mwedzi mipfumbamwe nemazuva gumi nemashanu, mukukwezva 11; gare gare gore iro, akarova chibodzwa chake chekutanga muSerie A mukukwezva 22 kumba neSampdoria musi wa25 Gumiguru. Ndiye wechitatu mudiki mutambi munhoroondo kutanga muSerie A, kumashure chete Amedeo Amadei naPietro Pellegri, uye wechipiri mudiki zvibodzwa muSerie A, kumashure chete Amadei. Gore rakatevera, akatengwa ne AC Milan pachibvumirano chekudyidzana, semunhu anozotsiva kaputeni wekirabhu Juan Schiaffino muchinzvimbo chekutamba; kunyangwe vakuru vekirabhu vaishushikana nezvechimiro cheRivera panguva yekutongwa kwake, Schiaffino akasimbirira kuti mudiki ane tarenda apiwe kondirakiti, uye akazoshanda semurairidzi kune wechidiki anorwisa wepakati. Rivera akapedza mwaka wake wokutangaMukati memwaka, akarova chibodzwa mukukwikwidza 11 naMilan musi wa7 Kukadzi 1960, uye akatamba mitambo makumi maviri nematanhatu, umo akarova zvibodzwa zvitanhatu, zvakare achiwana zita remadunhurirwa rekuti Il Signorino murume mudiki. Kunyangwe Alessandria yakadzikiswa, kuita kwaRivera mumwaka wese kwakafadza Milan, uyo gare gare gore iro rakasaina mudiki kubva kuAlessandria kune mamwe mamirioni makumi matanhatu nemashanu, zvichiita kuti mari yake yekutumira panguva iyoyo ive mari inoshamisa yemamirioni zana nemakumi matatu emadhora; mari yekutumira yakabhadharwa neMilan kuAlessandria yaisanganisirawo kutengeswa kwaGiancarlo Migliavacca, naSergio Bettini pachikwereti. Kuonekwa kwekupedzisira kwaRivera neAlessandria kwakauya musi wa19 Chikumi 1960, mukukundwa kwe2-0 kumba vachipesana neFC La Chaux-de-Fonds muchikamu chekutanga cheCoppa delle Alpi. 