The Sooners (5-0, 2-0 Big 12) were clinging to a 13-10 lead when Clay's long TD with under 5 minutes remaining gave them a much-needed 10-point advantage.
The points proved to be crucial when TCU (2-3, 0-2) responded with a five-play, 74-yard drive capped by Trevone Boykin's 8-yard run for a touchdown, narrowing the gap to 20-17.
But Blake Bell iced the contest on the Sooners' next possession with 17-yard run for a first down and Oklahoma was then able to run out the clock.
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