| Week | Date | Rank | Rec | Points | FPV | CP | BCS | Last Week |
|---|---|---|---|---|---|---|---|---|
| 1 | Sep 3 | NR | 1-0 | 0 | 0 | RV | -- | W 58-14 vs Murray State |
| 4 | Sep 22 | RV | 3-0 | 2 | 0 | RV | -- | W 45-28 at Indiana |
| 5 | Sep 29 | RV | 4-0 | 14 | 0 | RV | -- | W 41-19 vs Arkansas State |
| 6 | Oct 6 | 25 | 5-0 | 105 | 0 | RV | -- | W 51-28 at Vanderbilt |
| 7 | Oct 13 | 14 | 6-0 | 749 | 0 | 14 | -- | W 41-26 at #7 Georgia |
| 8 | Oct 20 | 5 | 7-0 | 1197 | 0 | 7 | 5 | W 36-17 vs #22 Florida |
| 9 | Oct 27 | 10 | 7-1 | 873 | 0 | 10 | 9 | L 27-24 (2OT) vs #20 South Carolina |
| 10 | Nov 3 | 9 | 8-1 | 956 | 0 | 9 | 8 | W 31-3 vs Tennessee |
| 11 | Nov 10 | 9 | 9-1 | 1012 | 0 | 8 | 9 | W 48-17 at Kentucky |
| 12 | Nov 17 | 8 | 9-1 | 1067 | 0 | 8 | 8 | DNP |
| 13 | Nov 24 | 5 | 10-1 | 1202 | 0 | 6 | 5 | W 24-10 at #24 Mississippi |
| 14 | Dec 1 | 5 | 11-1 | 1281 | 0 | 5 | 5 | W 28-21 vs #19 Texas A&M |
| 15 | Dec 8 | 9 | 11-2 | 1066 | 0 | 9 | 8 | L 59-42 vs #3 Auburn (SEC CG) |
| Final | Jan 7 | 5 | 12-2 | 1236 | 0 | 5 | -- | W 41-31 vs #13 Oklahoma 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.