Doege, who threw three touchdowns the week before against Nevada and set an NCAA record with a 90.9 completion percentage against New Mexico, was 29 for 46. The 6-foot-1 redshirt junior, playing his first full season since high school in 2005, was also intercepted for the first time this season but still turned in another virtuoso performance for the Red Raiders (4-0) to remain among the country's top passers.
Kansas' Jordan Webb, who also came into the game without an interception in his first three games, was picked off three times and each turnover led directly to a Texas Tech TD.
Doege connected with Eric Ward on a 40-yard scoring pass, found Jacoby Franks for a 13-yard TD toss and made it 45-27 late in the third quarter with an 18-yard touchdown pass to Ward, who had 71 yards on four catches.
The Jayhawks (2-2) parlayed a bevy of big plays into 191 yards and three touchdowns on their first 15 plays of the defensively-challenged day. But then Doege and the Red Raiders got hot, scoring 24 unanswered points before Kansas got a 19-yard touchdown pass from Webb to Rell Lewis to take a 27-24 lead after a first half that lasted just 9 minutes short of 2 hours.
The Red Raiders, off to their first 4-0 start since beginning 10-0 in 2008, unleashed a 21-0 third-quarter blitz to salt away their 12th victory in 13 meetings with the Jayhawks.
Stephens tallied on runs of 8 and 1 yards before Ward's final touchdown catch following Cquilin Hubert's interception.
D.J. Beshears got Kansas rolling with a 56-yard return of the opening kickoff. Four plays later, James Sims broke loose up the middle on an 11-yard TD run. Terrance Bullitt blocked the extra point, leaving it 6-0.
On the Jayhawks' second possession, Brandon Bourbon broke into the Tech secondary on a counter play, slipped a tackle, and sped 51 yards into the end zone for Kansas' longest run of the year. Bourbon had 101 yards on 10 carries and Webb was 16 for 22 for 239 yards and three touchdowns.
Doege, who had thrown 122 passes this season without an interception, was picked off by safety Keeston Terry on Texas Tech's next possession and Kansas set up on its own 25. Beshears got 54 yards on a catch-and-run, then, from the 21, Webb connected with tight end Tim Biere.
He appeared to score, but fumbled at the goal line. Kale Pick recovered for Kansas in the end zone to make it three touchdowns on three possessions by the seven-point home underdogs.
DeAndre Washington got the Red Raiders' comeback started with a 1-yard touchdown run, capping a 7-play, 52-yard drive.
Then Webb, who had not thrown an interception in 61 passes this year, was picked off by safety D.J. Johnson. A chop block penalty shoved Tech back 15 yards to the Kansas 40, but Ward took Doege's pass at the 30 and weaved his way through a gauntlet of would-be tacklers for a second TD on the very next play.
Webb, who came into the game No. 2 on the Big 12's pass efficiency chart, threw a second straight interception to Johnson on his next pass. The Red Raiders needed six plays to cover 45 yards, with Franks scoring on a 13-yard reception for a 21-20 Tech lead.
Donnie Carona's 46-yard field goal put the Red Raiders ahead 24-20 with 7:54 left in a first half that saw the teams combine for 560 yards.