The Red Raiders backup quarterback was 33-for-41 and finished with TDs passes of 52, 6, 4, 72, 28, 12 and 25 yards to five receivers.
It was the second time this season that a Texas Tech (4-2, 1-1 Big 12) quarterback notched seven passing touchdowns. Taylor Potts, out with a concussion this week, threw seven in a 55-10 win over Rice.
Texas Tech put the game out of reach by halftime. The Wildcats (3-3, 1-1 Big 12) got into Texas Tech territory only once in the first half and punted five times.
Sheffield's first-half yardage set a school record, besting the 367 yards thrown by B.J. Symons against Mississippi in 2003.
Three Red Raiders receivers tallied 90 yards or more. Lewis caught eight passes for 100 yards, Franks had three passes for 99 yards and Swindall got 97 yards on five catches.
Sheffield threw to 11 receivers before leaving the game with about 10 minutes remaining in the game.
The Wildcats offense was anemic in the first half. They sustained only one drive in the first half, managing four first downs and hanging onto the ball for more than six minutes on their opening possession. Grant Gregory got sacked three times-twice by Brandon Sharpe and once by Ra'Jon Henley-before Carson Coffman replaced him late in the second quarter.
Kansas State's first score came from its defense. Sheffield threw an interception on his first pass of the second half when Wildcats end Jeffrey Fitzgerald stepped in front of a ball meant for Alex Torres and returned it 17 yards to make it 38-7.
It wasn't until quarterback Carson Coffman replaced Gregory that the Wildcats showed some life. He was 11-for-17 and finished with 131 passing yards.
Coffman found some success in the third quarter but it didn't translate into a touchdown. After a 52-yard pass to Daniel Thomas and a 29-yarder to Jeron Mastrud, the Wildcats failed on a fourth-and-5 and gave the ball back to the Red Raiders.
Kansas State scored its second touchdown-and its only offensive one- midway through the fourth quarter when Keithen Valentine ran for an 8-yard touchdown to whittle the margin to 59-14.
Valentine rushed for a career-high 96 yards on eight carries.
Kansas State returns to action next Saturday when the Wildcats return home to face Texas A&M (3-2, 0-1 Big 12) at Bill Snyder Family Stadium at 6 p.m. The game will be broadcast on Fox College Sports.