1958–59 Yugoslav Cup
The 1958–59 Yugoslav Cup was the 12th season of the top football knockout competition in SFR Yugoslavia, the Yugoslav Cup, also known as the "Marshal Tito Cup", since its establishment in 1946.In the following tables winning teams are marked in bold; teams from outside top level are marked in italic script.
| Tie no | Home team | Score | Away team |
| 1 | Borac Banja Luka | 2–3 | Lokomotiva |
| 2 | Borac Čačak | 0–3 | Radnički Belgrade |
| 3 | Borovo | 1–0 | Sarajevo |
| 4 | Budućnost Titograd | 3–2 | Sutjeska Nikšić |
| 5 | Dinamo Zagreb | 3–2 | Proleter Osijek |
| 6 | Garnizon JNA Borac | 6–1 | Šibenik |
| 7 | Novi Sad | 2–2 | Partizan |
| 8 | Odred Ljubljana | 1–3 | Rijeka |
| 9 | OFK Belgrade | 1–2 | Željezničar Sarajevo |
| 10 | Pelister Bitola | 2–3 | Radnički Kragujevac |
| 11 | Radnički Sombor | 3–1 | Vardar |
| 12 | Red Star | 4–1 | Elektrostroj Zagreb |
| 13 | Trešnjevka | 2–3 | Vojvodina |
| 14 | Varteks | 5–0 | Rabotnički |
| 15 | Velež' | 5–0 | Radnički Niš |
Second round
Quarter-finals
Semi-finals
Final
