| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| Pre | Aug 12 | 11 | 0-0 | 927 | 0 | 11 | -- | DNP |
| 1 | Sep 3 | 9 | 1-0 | 968 | 0 | 10 | -- | W 51-0 vs Murray State |
| 2 | Sep 8 | 6 | 2-0 | 1125 | 0 | 8 | -- | W 38-0 vs Buffalo |
| 3 | Sep 15 | 7 | 3-0 | 1127 | 0 | 8 | -- | W 27-21 vs #24 Boston College |
| 4 | Sep 22 | 11 | 4-0 | 1009 | 0 | 11 | -- | W 30-27 (1OT) vs Vanderbilt |
| 5 | Sep 29 | 9 | 4-0 | 1085 | 0 | 9 | -- | DNP |
| 6 | Oct 6 | 21 | 4-1 | 352 | 0 | 18 | -- | L 41-10 at #25 Texas A&M |
| 7 | Oct 13 | 19 | 5-1 | 409 | 0 | 16 | -- | W 45-3 at Massachusetts |
| 8 | Oct 20 | 21 | 6-1 | 359 | 0 | 17 | -- | W 21-17 vs Auburn |
| 9 | Oct 27 | 25 | 6-2 | 44 | 0 | 23 | -- | L 34-0 at #15 Alabama |
| 10 | Nov 3 | RV | 81 | 0 | 22 | 24 | DNP | |
| 11 | Nov 10 | 24 | 7-2 | 176 | 0 | 21 | 23 | W 30-23 vs Oklahoma |
| 12 | Nov 17 | RV | 56 | 0 | RV | 23 | L 34-30 at #23 South Carolina | |
| 13 | Nov 24 | 24 | 8-3 | 142 | 0 | 24 | 21 | W 39-20 at Mississippi State |
| 14 | Dec 1 | 22 | 9-3 | 214 | 0 | 20 | 19 | W 28-21 vs Arkansas |
| 15 | Dec 8 | 23 | 9-3 | 228 | 0 | 20 | 19 | DNP |
| Final | Jan 21 | 22 | 10-3 | 266 | 0 | 20 | -- | W 27-24 vs Iowa (Music City Bowl) |
Note: Missouri's ranking in the final 1961 poll has been changed to unranked after the original AP wire story and poll was revisited and confirmed across several newspapers.