| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| Pre | Aug 17 | 24 | 0-0 | 134 | 0 | RV | -- | DNP |
| 1 | Sep 2 | 24 | 1-0 | 147 | 0 | 22 | -- | W 38-18 vs South Dakota State |
| 2 | Sep 7 | 20 | 2-0 | 237 | 0 | 22 | -- | W 49-24 at Toledo |
| 3 | Sep 14 | 18 | 3-0 | 446 | 0 | 19 | -- | W 38-10 vs UCF |
| 4 | Sep 21 | RV | 3-1 | 5 | 0 | RV | -- | L 31-27 vs Indiana |
| 5 | Sep 28 | 24 | 4-1 | 145 | 0 | RV | -- | W 21-20 at #13 South Carolina |
| 6 | Oct 5 | 23 | 4-1 | 212 | 0 | 24 | -- | DNP |
| 7 | Oct 12 | NR | 4-2 | 0 | 0 | RV | -- | L 34-0 vs #13 Georgia |
| 8 | Oct 19 | RV | 5-2 | 4 | 0 | RV | -- | W 42-13 at Florida |
| 9 | Oct 26 | RV | 6-2 | 7 | 0 | RV | NR | W 24-14 vs Vanderbilt |
| 10 | Nov 2 | RV | 7-2 | 42 | 0 | RV | NR | W 20-10 vs Kentucky |
| 11 | Nov 9 | RV | 7-2 | 68 | 0 | RV | NR | DNP |
| 12 | Nov 16 | 19 | 8-2 | 376 | 0 | 20 | 20 | W 34-27 at Texas A&M |
| 13 | Nov 23 | 17 | 9-2 | 525 | 0 | 17 | 17 | W 29-21 at Tennessee |
| 14 | Nov 30 | 14 | 10-2 | 740 | 0 | 13 | 16 | W 21-14 vs Arkansas |
| 15 | Dec 7 | 16 | 10-3 | 599 | 0 | 14 | 16 | L 42-13 vs #1 Alabama (SEC CG) |
| Final | Jan 13 | 14 | 11-3 | 710 | 0 | 11 | -- | W 33-17 vs Minnesota (Citrus) |
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.