League campaign with O'Shea capturing a first National Football League winners' medal. He subsequently captured a first Munster title at senior level following a win over Cork. Kerry later took on Dublin for the third consecutive year; however, this time it was in the All-Ireland semi-final. In one of the greatest games of football ever-played 'The Dubs' triumphed and O'Shea was still left waiting for a senior All-Ireland final appearance. In 1978, Kerry faced little competition in the provincial championship once again. A defeat of Cork gave O'Shea a second consecutive Munster title. Kerry later qualified for a third All-Ireland final in four years. Old rivals Dublin provided the opposition, however, the game turned into a rout. The game is chiefly remembered for Mikey Sheehy's sensational goal. The Kerry forward lobbed the ball over the head of Paddy Cullen, who was caught off his line arguing with the referee. Eoin Liston announced his arrival on the inter-county scene and scored a hat-trick of goals. Pat Spillane played all over the field, including goalkeeper after Charlie Nelligan was sent off. At the full-time whistle, Kerry were the winners by a 5–11 to 0–9 scoreline. In 1979, Kerry made it five-in-a-row in Munster as Cork fell by ten points in the provincial final. It was O'Shea's third Munster title. He later went in search of a second consecutive All-Ireland medal. Dublin provided the opposition for the fifth consecutive occasion. Kerry were handicapped throughout the game. Ger Power did not start the game, while John O'Keeffe got injured and Páidí Ó Sé was sent off during the encounter. Two goals by Mikey Sheehy and a third by John Egan helped 'The Kingdom' to a 3–13 to 1–8 victory. It was O'Shea's second All-Ireland winners' medal. Kerry's dominance continued in 1980. Another defeat of Cork in the provincial final gave O'Shea a fourth Munster winners' medal in succession. Another All-Ireland final appearance beckoned, this time with Roscommon providing the opposition. The Connacht champions shocked Kerry and took a five-point lead inside the first twelve minutes. Mikey Sheehy popped up again to score the decisive goal, as Kerry went on to claim a 1–9 to 1–6 victory in a game that contained sixty-four frees. The victory gave Kerry and O'Shea a third All-Ireland title in succession. He finished off the impressive year by collecting the Texaco Footballer of the Year award. In 1981, O'Shea won