Surprise of the tournament were second-level side Galenika from Zemun, who managed to reach the semi-finals, knocking out the remaining two of the Yugoslav "Big Four" clubs Partizan and Hajduk Split in the process.
The cup final was played over two legs on 16 and 23 May, traditionally scheduled to coincide with Youth Day celebrated on 25 May, a national holiday in Yugoslavia which also doubled as the official commemoration of Josip Broz Tito's birthday.
Sixteen out of eighteen 1981–82 Yugoslav First League clubs entered the competition at this stage (everyone except Osijek and Teteks, who were only promoted to top level at the end of the 1980–81 season).
In addition, Croatia Zürich, a Zürich-based club ran by Croatian emigrants in Switzerland, also received a spot, but exited the tournament following a 5–0 defeat to Budućnost.
Seven top-level clubs were knocked out at this stage: OFK Belgrade, Partizan, Radnički Niš, Vardar, Zagreb and the defending cup winners Velež, who lost their tie to Montenegrin minnows Mogren on penalties.
Red Star, Dinamo Zagreb and Sloboda progressed to the semi-finals, along with Zemun-based Galenika - who were the only team from outside top flight left in the competition after this stage.
It was won by a squad featuring major club stars such as Vladimir Petrović, Dušan Savić, Miloš Šestić and Milko Đurovski, led by experienced coach Branko Stanković.
Dinamo's squad that season featured club legends such as Snješko Cerin, Velimir Zajec, Zlatko Kranjčar, Marko Mlinarić and Stjepan Deverić.
Savić, who had spent the first leg in Zagreb on the substitute bench, used runs down the right side to create several goalscoring opportunities for Rajko Janjanin and Vladimir Petrović very early on, but Dinamo's goalkeeper Tomislav Ivković was on form and saved a couple of close-range efforts.