Fitzgibbon was selected for the Cork senior team for the first time on 8 June 1986. He was an unused substitute for the 6-13 to 0-09 defeat of Waterford in the Munster Championship. After impressing in a series of challenge matches, Fitzgibbon was named at right corner-forward for the Munster final against Clare. He scored 1-01 from play in the 2-18 to 3-12 victory. He was dropped from the starting fifteen for the subsequent All-Ireland Championship. On 7 September, Fitzgibbon won an All-Ireland medal as a non-playing substitute in Cork's 4-13 to 2-15 defeat of Galway in the final.