Lyle Leong snared three touchdown passes from Harrell, who was 38-for-51 for 454 yards. Texas Tech (5-0, 1-0 Big 12), with its highest ranking in 32 years, scored on seven straight possessions and did not attempt a punt until Stefan Loucks replaced Harrell late in the fourth quarter.
The Red Raiders rolled up 626 yards of total offense.
Leong had scoring catches of 1 yard in the first quarter, 15 in the second and 7 in the third against the outmanned Wildcats (3-2, 0-1). Michael Crabtree had nine catches for 107 yards and two TDs.
The Red Raiders, leading the nation in total offense (572.8 yards per game), and passing (426.2), had 417 and 316 while putting up a 38-14 halftime lead over a Kansas State defense which the week before had yielded 300 yards rushing to Louisiana-Lafayette.
The six TD passes tied the career-best for Harrell, who spread his passes around to 10 different receivers. The three-year starter ran his career total to 12,709 yards, erasing the record of 12,429 yards by Kliff Kingsbury from 1999-02.
Harrell had five touchdown passes in the first half. He got the school record for career passing yards with a 15-yard completion to Adam James and a moment later made it 24-14 with a thread-the-needle 15-yard strike to Leong, who made the catch in double coverage and twisted into the corner of the end zone.
Facing fourth-and-inches from their own 29 late in the first quarter, the Red Raiders sent Shannon Woods on a sweep. But he was stuffed, and four plays later, Kansas State quarterback Josh Freeman scored on a 1-yard run, knotting the game 14-all.
But after that, the sunny, wind-swept day belonged entirely to Tech. With Harrell enjoying all the time he needed to pick and choose from a bevy of receivers, the Red Raiders scored a field goal and six touchdowns on their next seven possessions.
They took a 52-21 lead on the third play of the fourth quarter when Harrell bulled into the end zone on a 1-yard keeper on fourth down.
Earlier in the drive, the Red Raiders went for it on fourth-and-4 from the 46 and Harrell's pass was incomplete. But an offsides penalty on Kansas State was immediately followed by a 30-yard gain to Tramain Swindall.
On successive possessions in the second quarter, Harrell led quick-hitting drives of 53, 70 and 54 yards. Freeman, in the meantime, went cold, misfiring on 9 of 10 passes, several of which Tech defenders got their hands on.
The Kansas State junior, who a week earlier had become his own school's career passing leader, was 13-for-28 for 170 yards, including a 33-yard TD pass to Ernie Pierce. Pierce also scored on an 18-yard return of a blocked punt late in the game.