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.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.