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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.