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.
High school junior Zach Brown, a 7-footer from Miami, has rescinded his commitment to UConn, sources told ESPN.
Reserve center Akolda Manyang has been charged with felony aggravated assault after being accused of punching a man in the face without provocation.
Should the 76ers take Ben Simmons No. 1? What if they get the Lakers' pick, too? And how does the rest of the top 10 shake out? Our Insiders run their latest mock draft, with Philly on the clock.