| Game |
| Result | Moves |
Year |
Event/Locale | Opening |
| 1. Randviir vs Keres |
| 0-1 | 26 |
1943 |
Tallinn ,Est ch (21.07.43) | B20 Sicilian |
| 2. Randviir vs Keres |
| 0-1 | 20 |
1945 |
Tallinn ,Est op ch (30.09.45) | C36 King's Gambit Accepted, Abbazia Defense |
| 3. Randviir vs Keres |
| 0-1 | 63 |
1947 |
Parnu tt (19.07.47) | C45 Scotch Game |
| 4. R Renter vs Randviir |
| ½-½ | 30 |
1947 |
Parnu it | D48 Queen's Gambit Declined Semi-Slav, Meran |
| 5. Boleslavsky vs Randviir |
| 1-0 | 22 |
1947 |
Parnu it | B10 Caro-Kann |
| 6. Randviir vs V Makogonov |
 | 0-1 | 57 |
1947 |
Parnu it | B10 Caro-Kann |
| 7. Randviir vs Kotov |
| 0-1 | 41 |
1947 |
Estonia | B10 Caro-Kann |
| 8. Kasparian vs Randviir |
| 1-0 | 52 |
1947 |
Parnu it | D13 Queen's Gambit Declined Slav, Exchange Variation |
| 9. Randviir vs Bondarevsky |
| ½-½ | 41 |
1947 |
Parnu it | C01 French, Exchange |
| 10. Randviir vs Bronstein |
| 0-1 | 41 |
1947 |
Parnu it | C45 Scotch Game |
| 11. Smyslov vs Randviir |
 | 1-0 | 39 |
1947 |
Tournament, Parnu (Estonia) | C64 Ruy Lopez, Classical |
| 12. Lilienthal vs Randviir |
| 1-0 | 20 |
1947 |
Parnu it | B17 Caro-Kann, Steinitz Variation |
| 13. Tolush vs Randviir |
 | 1-0 | 44 |
1947 |
Parnu it | D47 Queen's Gambit Declined Semi-Slav |
| 14. Randviir vs Simagin |
| 1-0 | 56 |
1947 |
Tournament | B71 Sicilian, Dragon, Levenfish Variation |
| 15. Randviir vs Flohr |
 | 0-1 | 27 |
1947 |
Parnu it | B17 Caro-Kann, Steinitz Variation |
| 16. Randviir vs Ufimtsev |
| 1-0 | 73 |
1949 |
Ch URS (1/2 final) | B92 Sicilian, Najdorf, Opocensky Variation |
| 17. Randviir vs Levenfish |
| 0-1 | 84 |
1949 |
Ch URS (1/2 final) | C45 Scotch Game |
| 18. Taimanov vs Randviir |
| ½-½ | 25 |
1949 |
Leningrad | D31 Queen's Gambit Declined |
| 19. Randviir vs Estrin |
 | 1-0 | 78 |
1949 |
URS-ch sf | C45 Scotch Game |
| 20. Randviir vs Zamikhovsky |
| ½-½ | 42 |
1949 |
URS-ch sf | B10 Caro-Kann |
| 21. Randviir vs Keres |
| 0-1 | 51 |
1953 |
Tartu ,Est op ch (03.04.53) | B50 Sicilian |
| 22. Tal vs Randviir |
| ½-½ | 25 |
1955 |
Vilnius | D10 Queen's Gambit Declined Slav |
| 23. Randviir vs I Nei |
| ½-½ | 19 |
1955 |
URS-ch sf | B22 Sicilian, Alapin |
| 24. Randviir vs Keres |
| ½-½ | 24 |
1955 |
Parnu (28.07.55) | C77 Ruy Lopez |