Kore White's tip-in of a missed 3-pointer by Poland broke a 49-49 tie with 3:17 remaining, starting an 8-0 run for the Bulls (4-2), who played their first road game this season.
The Hatters (2-2) had run off seven straight points, five by Aaron Graham, to erase a 47-40 Bulls lead.
Poland grabbed 10 rebounds and Fitzpatrick nine for the Bulls, who outrebounded Stetson 41-31.
Joel Naburgs led Stetson with 18 points and Graham added 15.
Each team was missing a key player. South Florida's Anthony Collins, who had 22 assists in his past two games, rested a calf injury but should play Friday against Georgia. Stetson's leading scorer, Adam Pegg, sat out a one-game Atlantic Sun Conference suspension for a level 2 flagrant foul in his last game.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.