| Game |
| Result | Moves |
Year | Event/Locale | Opening |
| 51. A Bannik vs J Randviir |
| ½-½ | 51 | 1955 | 4th Soviet Team-ch final | D11 Queen's Gambit Declined Slav |
| 52. Taimanov vs J Randviir |
| 1-0 | 35 | 1955 | 4th Soviet Team-ch final | D45 Queen's Gambit Declined Semi-Slav |
| 53. J Randviir vs A Sokolsky |
| 0-1 | 51 | 1956 | URS-ch qf Tallinn | B10 Caro-Kann |
| 54. J Randviir vs I Nei |
| ½-½ | 13 | 1956 | URS-ch qf Tallinn | C13 French |
| 55. J Randviir vs P Kampenuss |
| 1-0 | 30 | 1956 | URS-ch qf Tallinn | B09 Pirc, Austrian Attack |
| 56. J Randviir vs I Vistaneckis |
| 0-1 | 79 | 1956 | URS-ch qf Tallinn | C45 Scotch Game |
| 57. G Uusi vs J Randviir |
| 1-0 | 41 | 1957 | Estonian Championship | E18 Queen's Indian, Old Main line, 7.Nc3 |
| 58. Lutikov vs J Randviir |
| 1-0 | 34 | 1958 | 5th Soviet Team Championship Final | D11 Queen's Gambit Declined Slav |
| 59. Tolush vs J Randviir |
| 1-0 | 40 | 1958 | 5th Soviet Team Championship Final | D51 Queen's Gambit Declined |
| 60. J Randviir vs Furman |
| ½-½ | 9 | 1959 | 2nd Soviet Spartakiad qual-3 | B30 Sicilian |
| 61. J Randviir vs V Konovalov |
| 1-0 | 22 | 1959 | 2nd Soviet Spartakiad qual-3 | B06 Robatsch |
| 62. J Randviir vs A Shagalovich |
| ½-½ | 19 | 1959 | 2nd Soviet Spartakiad Final-B | C02 French, Advance |
| 63. V Barsauskas vs J Randviir |
| 0-1 | 22 | 1959 | 2nd Soviet Spartakiad Final-B | A13 English |
| 64. J Randviir vs A Blagidze |
| 1-0 | 39 | 1961 | Baltic Republics Championship | B10 Caro-Kann |
| 65. Koblents vs J Randviir |
| ½-½ | 41 | 1961 | Baltic Republics Championship | C41 Philidor Defense |
| 66. I Nei vs J Randviir |
| ½-½ | 13 | 1961 | Baltic Republics Championship | D10 Queen's Gambit Declined Slav |
| 67. J Randviir vs A Buslaev |
| ½-½ | 17 | 1961 | Baltic Republics Championship | A04 Reti Opening |
| 68. J Klavins vs J Randviir |
| 0-1 | 40 | 1961 | Baltic Republics Championship | A06 Reti Opening |
| 69. J Randviir vs I Zilber |
| ½-½ | 18 | 1961 | Baltic Republics Championship | A06 Reti Opening |
| 70. J Randviir vs D Lapienis |
| ½-½ | 10 | 1961 | Baltic Republics Championship | B50 Sicilian |
| 71. V Mikenas vs J Randviir |
| ½-½ | 44 | 1961 | Baltic Republics Championship | C41 Philidor Defense |
| 72. U Tarve vs J Randviir |
| 1-0 | 78 | 1961 | Estonian Championship | B17 Caro-Kann, Steinitz Variation |
| 73. L Maslov vs J Randviir |
| 0-1 | 26 | 1961 | Baltic Republics Championship | A11 English, Caro-Kann Defensive System |
| 74. J Randviir vs T Oim |
| ½-½ | 12 | 1961 | Baltic Republics Championship | C42 Petrov Defense |
| 75. J Randviir vs A Petersons |
| ½-½ | 30 | 1961 | Baltic Republics Championship | A04 Reti Opening |
Kibitzing
