Following a 14-14 tie after the first quarter, Tech scored 42 points on six straight possessions.
Harrell, a senior from Ellis, Texas, finished with 34 completions in 42 pass attempts for 386 yards. His one-yard touchdown run with 8:23 left in the third gave the unbeaten Red Raiders (8-0, 4-0 Big 12) a 42-14 advantage.
All-America wide receiver Michael Crabtree scored twice after nine receptions for 70 yards. Fellow wideout Eric Morris also scored twice, while Edward Britton scored once on three receptions for 106 yards.
Kansas quarterback Todd Reesing was 16-of-26 for 154 yards with two touchdowns, but three interceptions.
Jocques Crawford scored once, and Jake Sharp gained 80 yards on 13 carries for the Jayhawks (5-3, 2-2), who lost their homecoming contest and have lost two in a row after a three-game winning streak.