In 2001 Dunne was captain of the Tipperary team for a third consecutive year. That year Tipp made a third consecutive appearance in the National League final. After one victory and one defeat Dunne's side were successful again and defeated Clare by 1–19 to 0–17. It was Dunne's third winners' medal in that competition. Later that year Tipp contested the Munster final. It was Dunne's fourth time lining out in a provincial decider, however, he had yet to end up on the winning side. All this changed in 2001 when Tipperary defeated Limerick by 2–16 to 1–17. It was Dunne's first Munster title. After a draw and a replay against Wexford Dunne later led his team out in Croke Park on All-Ireland final day. Galway provided the opposition on that occasion; however, two goals by Tipp's Mark O'Leary gave the Munster men the threshold to withstand a Galway comeback. With nine minutes to go Dunne's side only led by one point, however, Tipperary outscored Galway by five to three in those closing minutes. At the final whistle Tipperary were the winners by 2–18 to 2–15. Not only did Dunne collect his first, and only, All-Ireland medal but he also had the honour of collecting the Liam MacCarthy Cup on behalf of his team and county. A third All-Star award quickly followed while Dunne also picked up all three Hurler of the Year awards.