Clarke connected on three 3-pointers for Butler (24-7, 11-5 Atlantic 10), and converted 8 of 8 free-throw attempts.
Samaj Christon scored 20 points to lead Xavier (17-13, 9-10), and Isaiah Philmore scored 16 points and grabbed 11 rebounds.
Woods' effort helped Xavier build a 36-13 scoring advantage off the bench.
Butler's largest lead of the game was 10 points, Xavier's was 4.
Clarke scored 17 of his points in the second half. Woods totaled 10 of his points after intermission.