The 1971–72 season of the European Cup Winners' Cup football club tournament was won by Rangers, who defeated Dynamo Moscow in the final.
Preliminary round
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First leg
Second leg
4–4 on aggregate; Austria Wien won on away goals.
Hibernians won 3–2 on aggregate.
First round
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First leg
Second leg
Barcelona won 7–1 on aggregate.
Steaua București won 1–0 on aggregate.
Liverpool won 3–2 on aggregate.
Bayern Munich won 7–1 on aggregate.
Torino won 5–0 on aggregate.
Austria Wien won 2–1 on aggregate.
Rangers won 2–1 on aggregate.
Sporting CP won 7–0 on aggregate.
Åtvidaberg won 5–4 on aggregate.
Chelsea won 21–0 on aggregate.
Beerschot won 8–0 on aggregate.
2–2 on aggregate; BFC Dynamo won 5–4 on penalties.
Sparta won 3–1 on aggregate.
Red Star Belgrade won 8–4 on aggregate.
Eskişehirspor won 4–0 on aggregate.
Dynamo Moscow won 3–2 on aggregate.
Second round
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1The second leg was originally 3–2 to Sporting after 90 minutes, and 4–3 to Sporting after extra time. The referee erroneously ordered a penalty shoot-out which Sporting won 3–0; UEFA later ruled that Rangers had won on away goals.
First leg
Second leg
Steaua București won 3–1 on aggregate.
Torino won 1–0 on aggregate.
6–6 on aggregate; Rangers won on away goals.
BFC Dynamo won 6−2 on aggregate.
Quarter-finals
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First leg
Second leg
1–1 on aggregate; Bayern Munich won on away goals.
Rangers won 2–1 on aggregate.
BFC Dynamo won 4−2 on aggregate.
Semi-finals
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First leg
Second leg
Rangers won 3–1 on aggregate.
2–2 on aggregate; Dynamo Moscow won 4–1 on penalties.