| Week | Date | Rank | Rec | Points | FPV | CP | CFP | Last Week |
|---|---|---|---|---|---|---|---|---|
| Pre | Aug 11 | RV | 0-0 | 33 | 0 | NR | -- | DNP |
| 1 | Sep 2 | RV | 42 | 0 | RV | -- | W 61-6 vs Central Arkansas | |
| 2 | Sep 7 | 25 | 2-0 | 109 | 0 | RV | -- | W 42-31 vs Kansas |
| 3 | Sep 14 | 23 | 3-0 | 292 | 0 | 22 | -- | W 52-10 vs Louisiana |
| 4 | Sep 21 | 20 | 4-0 | 452 | 0 | 19 | -- | W 29-20 vs South Carolina |
| 5 | Sep 28 | 19 | 5-0 | 528 | 0 | 18 | -- | W 42-6 vs Massachusetts |
| 6 | Oct 5 | 14 | 5-0 | 775 | 0 | 14 | -- | DNP |
| 7 | Oct 12 | 16 | 5-1 | 649 | 0 | 16 | -- | L 27-24 vs #8 Alabama |
| 8 | Oct 19 | 15 | 6-1 | 748 | 0 | 14 | -- | W 23-17 (2OT) at Auburn |
| 9 | Oct 26 | 19 | 6-2 | 447 | 0 | 20 | -- | L 17-10 at #10 Vanderbilt |
| 10 | Nov 2 | 19 | 6-2 | 491 | 0 | 17 | 22 | DNP |
| 11 | Nov 9 | RV | 6-3 | 59 | 0 | 24 | NR | L 38-17 vs #3 Texas A&M |
| 12 | Nov 16 | 23 | 7-3 | 173 | 0 | 21 | 22 | W 49-27 vs Mississippi State |
| 13 | Nov 23 | RV | 7-4 | 23 | 0 | RV | NR | L 17-6 at #8 Oklahoma |
| 14 | Nov 30 | 25 | 8-4 | 73 | 0 | RV | NR | W 31-17 at Arkansas |
| 15 | Dec 7 | 25 | 8-4 | 92 | 0 | RV | NR | DNP |
| Final | Jan 20 | RV | 8 | 0 | RV | -- | L 13-7 vs #20 Virginia (Gator 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.