Tech (2-1) scored on five straight possessions after trailing TCU 21-0 midway through the second quarter.
With the Red Raiders ahead 56-21, TCU (2-1) rallied for two quick touchdowns to narrow the margin to 56-35 with about 11 minutes left in the game.
That was as close as the Horned Frogs could get.
Cumbie, who led the nation in passing coming into the game, hit on 30-of-60 passes and threw two interceptions. He is averaging 453 passing yards in his first three college starts.
Henderson ran for TDs of 4, 6 and 2 yards.
Red Raiders receiver Jarrett Hicks, who was third in the nation in receiving yards per game coming in, had his third straight game of 150 yards or more. He caught eight passes for 211 yards and is averaging 170 yards per game.
It was the Horned Frogs' first visit to Lubbock since 1995. They lost that game 27-6. They later joined Conference USA, while Texas Tech became a member of the Big 12.
The loss ended TCU quarterback Tye Gunn's winning streak as a starter at 10. He had been chasing the school record of 12 straight set by Hall of Famer Sammy Baugh.
Initially, the Red Raiders had difficulty sustaining drives. On its first seven possessions, the closest Tech got was the TCU 29, where they failed on a fourth-and-2 on a pass attempt from Cumbie to Hicks.
Down by 21, Tech didn't score until its eighth possession when Henderson ran for a 4-yard TD with 6:53 remaining in the second quarter.
Tech pulled within 21-14 when Cumbie threw a short shovel pass to Johnnie Mack from the 8. The TD was set up by Danny Amendola's 52-yard put return to TCU's 3. A celebration penalty put the Red Raiders at the 18 and three plays later they scored.
Cumbie leveled it at 21 on the closing drive of the first half, capping a 65-yard drive with a 4-yard pass to Bristol Olomua.
Tech never trailed after that and even got points from its defense. With about nine minutes remaining in the third quarter, Adell Duckett forced a fumble from backup quarterback Brandon Hassell and Keyunta Dawson recovered it and went in for the score to make it 42-21.
Down by 35 in the fourth quarter, TCU scored two touchdowns in 15 seconds. Lonta Hobbs scooted for 61 yards and a TD and the Horned Frogs trailed 56-28. On Tech's next possession, Mark Walker intercepted Cumbie's pass in Tech territory. Hassell threw a 22-yard pass to Quentily Harmon to cut the margin to 56-35.
Texas Tech Takes TCU, 70-35
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