| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| 1 | Sep 13 | RV | 0-0 | 3 | 0 | NR | -- | DNP |
| 5 | Oct 11 | RV | 1-2 | 2 | 0 | RV | -- | W 45-41 vs #17 LSU |
| 6 | Oct 18 | NR | 1-2 | 0 | 0 | RV | -- | DNP |
| 7 | Oct 25 | NR | 2-2 | 0 | 0 | RV | -- | W 20-10 vs Kentucky |
| 8 | Nov 1 | NR | 2-3 | 0 | 0 | RV | -- | L 41-17 at #10 Florida |
| 9 | Nov 8 | NR | 2-3 | 0 | 0 | RV | -- | DNP |
| 10 | Nov 15 | NR | 2-3 | 0 | 0 | RV | -- | DNP |
| 11 | Nov 22 | NR | 3-3 | 0 | 0 | NR | NR | W 17-10 at South Carolina |
| 12 | Nov 29 | NR | 4-3 | 0 | 0 | RV | NR | W 41-0 vs Vanderbilt |
| 13 | Dec 6 | RV | 5-3 | 8 | 0 | RV | 25 | W 50-48 vs Arkansas |
| 14 | Dec 13 | NR | 5-4 | 0 | 0 | RV | NR | L 49-14 vs #12 Georgia |
| Final | Jan 12 | NR | 0 | 0 | RV | -- | DNP |
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.