Leading off the inning, Zach Diewert was hit by a pitch. He stole second and took third when the catcher's throw sailed into center field.
With the infield in for a possible play at the plate, Cullum hit a high chopper over the third baseman's head, bringing Diewert home with the winning run.
South Florida took a 1-0 lead in the top of the first on a single, an error, and a fielder's choice.
The Eagles answered with a run in the bottom of the inning. Bradley Harmon led off with a walk, raced to third on a wild throw to first base on a pickoff attempt, and scored on a wild pitch.
In the third, the Panthers took a 2-1 lead on back-to-back doubles.
A two-out rally tied the score at 2 in the sixth. Diewert doubled to left field and scored on Scott's single.
Luis Ferrer (6-1) earned the win in relief. He struck out four and held the Panthers hitless.
Shameko Smith started and worked six innings, allowing two runs on six hits while walking two and striking out eight.
The Eagles had seven hits.
Zach Biermann went 2-for-3.
Skylar Frey singled, walked, and stole a base.
Diewert went 2-for-3 with a double, a stolen base, and two runs.
Scott had a single, a walk, and an RBI.
The Eagles (24-8, 8-3, No. 2 FCSAA, No. 10 NJCAA) play South Florida again Monday at 6 p.m. in Avon Park.