| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| Pre | Aug 14 | NR | 0 | 0 | RV | -- | DNP | |
| 1 | Sep 5 | NR | 0 | 0 | RV | -- | W 35-10 vs South Dakota | |
| 2 | Sep 10 | NR | 0 | 0 | RV | -- | W 23-19 vs Middle Tennessee | |
| 3 | Sep 17 | RV | 72 | 0 | RV | -- | W 30-27 vs #15 Kansas State | |
| 4 | Sep 24 | 23 | 4-0 | 197 | 0 | 22 | -- | W 34-27 vs Memphis |
| 5 | Oct 1 | 21 | 5-0 | 329 | 0 | 22 | -- | W 38-21 at Vanderbilt |
| 6 | Oct 8 | RV | 69 | 0 | 25 | -- | L 49-39 vs #23 LSU | |
| 7 | Oct 15 | 20 | 6-1 | 365 | 0 | 20 | -- | W 38-21 at #24 Kentucky |
| 8 | Oct 22 | 16 | 7-1 | 594 | 0 | 16 | -- | W 34-12 vs South Carolina |
| 9 | Oct 29 | 14 | 7-1 | 714 | 0 | 14 | 12 | DNP |
| 10 | Nov 5 | 16 | 7-2 | 644 | 0 | 15 | 14 | L 30-21 at #1 Georgia |
| 11 | Nov 12 | 11 | 8-2 | 917 | 0 | 11 | 9 | W 36-7 vs #14 Tennessee |
| 12 | Nov 19 | 10 | 9-2 | 964 | 0 | 10 | 9 | W 33-31 vs Florida |
| 13 | Nov 26 | 9 | 10-2 | 1011 | 0 | 9 | 9 | W 48-14 at Arkansas |
| 14 | Dec 3 | 9 | 10-2 | 1014 | 0 | 9 | 9 | DNP |
| Final | Jan 9 | 8 | 11-2 | 1092 | 0 | -- | W 14-3 vs #7 Ohio State (Cotton) |
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.