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.