Clavell was pushing the ball for a final shot when Michael Bryson fouled him at midcourt while trying to steal the ball.
John Green hit a game-tying 3-pointer for UCSB (3-3) with 9 seconds left after Stanton Kidd and John Gillon each made 1 of 2 free throws in the final minute, extending the Colorado State (6-0) lead to 63-60.
The Rams took a 57-53 lead with 6:35 left on an 8-0 run.
Kidd led Colorado State with 14 points. Clavell, Gillon and J.J. Avila each scored 13. Daniel Bejarano had 10 points, 11 rebounds and four blocks.
Alan Williams led the Gauchos with 22 points, 12 rebounds and four blocks and Green added 12 points. Williams missed a 25-footer at the buzzer