The Red Raiders quelled an inspired A&M effort to overcome a 23-20 halftime deficit by limiting A&M to just two second-half points.
Harrell completed 44-of-56 passes for 450 yards, three touchdowns and two interceptions. He also ran for two fourth-quarter scores.
Tramain Swindall caught seven passes for 101 yards, Detron Lewis caught nine passes for 92 yards, Michael Crabtree scored twice after eight catches for 71 yards, and Baron Batch added 87 yards on 13 carries with one touchdown for the Red Raiders (7-0, 3-0 Big 12).
A&M's Jerrod Johnson completed 26-of-39 passes for 283 yards.
Mike Goodson and Stephen McGee both rushed for one touchdown, and Ryan Tannehill scored once after five catches for 104 yards for the Aggies (2-5, 0-3).
Texas Tech amassed 561 total yards to just 306 for the Aggies.