Jack Nunge added 16 points and nine rebounds and Zach Freemantle had 14 points and 11 rebounds for Xavier (4-1), which had five starters reach double-figure scoring. Kunkel finished with 11 points.
Trey Bonham, making his first start after transferring from VMI, led Florida (3-2) with 23 points and Will Richard, a Belmont transfer, added 18. Colin Castleton, who entered averaging 25.3 points per game, had 11 points, 10 rebounds and four assists, and Riley Kugel scored 12 points.
Xavier will face No. 8 Duke on Friday, while Florida faces Oregon State.
More AP college basketball: https://apnews.com/hub/college-basketball and https://apnews.com/hub/ap-top-25-college-basketball-poll and https://twitter.com/AP_Top25