Justin Hurtt led Tulsa (13-11, 6-4) with 23 points and four assists. Scottie Haralson added nine points but missed a potential game-winning 3-pointer at the buzzer.
The Knights didn't have a field goal the last 6 minutes of the game, but survived thanks to the free-throw shooting of Clanton and Jordan, who hit 7 of 8 from the line in the final minutes.
Clanton's two free throws gave UCF a 58-55 lead with 1:10 left, but Hurtt responded with two free throws for Tulsa with 45 seconds left to make it 58-57.
Jordan missed a driving layup with 8 seconds left, but Haralson couldn't connect from the corner.