He scored 14 goals in the 1970–71 campaign, the highest tally he ever recorded, including one in a 5–0 victory over Arsenal on 26 September that came third in the BBC Goal of the Season competition. The goal came after he played a one-two with Peter Dobing before striking a first-time shot into the net from 25-yards. Stoke reached the semi-finals of the FA Cup for the first time since 1899 in 1970–71, where they lost 2–0 to Arsenal after a replay; in the original tie Stoke had led 2–1 before conceding an equaliser five minutes into injury time. Conroy played in 19 of Stoke's 21 FA Cup and League Cup games in the 1971–72 season, as they reached the semi-finals of the FA Cup and the final of the League Cup. In the League Cup Stoke defeated Southport, Oxford United (after a replay), Manchester United (after two replays), Bristol Rovers and West Ham United (after two replays) to reach the Wembley final against Chelsea. Conroy was a key figure in the semi-final decider at Old Trafford against West Ham, as he won a penalty in the first half and then scored the winning goal on 49 minutes with a 25-yard volley. He also opened the scoring in the final itself, as he converted a simple header after five minutes, and helped Stoke to go on to secure the first trophy in the club's history with a 2–1 victory. Stoke also reached the semi-finals of the FA Cup, again losing to Arsenal, though Conroy missed this game as he was sidelined for the rest of the season after he injured his cartilage again in a defeat to Leeds United on 8 April.