Devonte Boykins' 3-pointer with six seconds left reduced North Carolina A&T's deficit to 88-85 before Rogers' dunk at the buzzer ended the game.
Ian Kinard made 1 of 2 free throws and South Carolina State led 87-77 with 22 seconds left.
Raymon Pratt made it a seven-point contest with a 3-point play with 12 seconds remaining before Kinard fouled him to send Pratt back to the foul line and he made both. Rogers made 1 of 2 free throws for an 88-82 lead before Boykins' 3.
South Carolina State (9-17, 5-6 Mid-Eastern Athletic Conference) got 13 points from Janai Rayner-Powell and 11 from James Richardson. South Carolina State led by double figures most of the second half.
Davaris McGowens led North Carolina A&T (15-10, 8-2) with 26 points and Boykins scored 13.
Mark Few: NCAA should have more urgency in corruption investigation
After NCAA president Mark Emmert said last week the investigation into corruption in college basketball wouldn't be completed anytime soon, Gonzaga Bulldogs coach Mark Few said he was "disappointed" in the NCAA's lack of urgency.
Kansas returns to No. 1 in AP poll as Gonzaga drops to 4th after loss
The preseason No. 1, the Jayhawks are again the top-ranked college basketball team in the AP Top 25 despite struggling to get past New Mexico State at home. Kansas slid into the top spot after previous No. 1 Gonzaga lost to Tennessee.
Miracle Kentucky shot, late rush in Eagles-Cowboys among weekend's worst gambling bad beats
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