As a sophomore in 1962, his first year on the varsity team, Sayers led the Big Eight Conference and was third in the nation with 1,125 rushing yards. His 7. 1 yards-per-carry average was the highest of any player in the NCAA that season. Against Oklahoma State, he carried 21 times for a conference single-game-record 283 yards to lead Kansas to a 36–17 comeback victory. In 1963, Sayers set an NCAA Division I FBS record with a 99-yard run against Nebraska. He finished the year with 917 rushing yards, again leading all rushers in the Big Eight. He earned first-team All-America recognition from the American Football Coaches Association (AFCA), the Football Writers Association of America (FWAA), the Newspaper Enterprise Association (NEA), The Sporting News, and United Press International (UPI), among others. In 1964, his senior year, he led the Jayhawks to a 15–14 upset victory over Oklahoma with a 93-yard return of the game's opening kickoff for a touchdown. He finished the year with 633 rushing yards, third most among Big Eight rushers, and also caught 17 passes for 178 yards, returned 15 punts for 138 yards, and returned seven kickoffs for 193 yards. He earned first-team All-America honors from each of the same selectors as in the previous year, in addition to the Associated Press (AP), among others.