The following season, Riva made his Serie A debut for Cagliari on 13 September, 1964, in a 2–1 loss against Roma, and also helped the club avoid relegation, leading the team to a comfortable sixth-place finish in the table, scoring an encouraging 9 goals in 32 appearances at the age of 20. This was followed by eleventh, sixth, and ninth place finishes in the league between 1965 and 1968, while Riva also finished as the league's top-scorer for the first time during the 1966–67 season with 18 goals, as the club began to build a potential title winning side around their star striker: Riva attracted several notable footballers to Cagliari, and the team during this period featured key players such as Enrico Albertosi, Roberto Boninsegna, Ricciotti Greatti, Comunardo Niccolai, Mario Martiradonna, Mario Brugnera, Pierluigi Cera, and Nené. Riva subsequently helped Cagliari to a second-place finish in both the Coppa Italia, behind Roma, and the league, four points behind Fiorentina, during the 1968–69 season, winning the "capocannoniere" title for a second time with 20 goals in 29 appearances; Cagliari had been leading in the league until the 21st matchday, when a loss at home to Juventus caused the team to surrender their lead.