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.
Huskies' Thybulle drops in a reverse dunk on alley-oop
Washington G Jaylen Nowell lobs a pass up to G Matisse Thybulle, who finishes with a one-handed reverse dunk.
Nowell scores 18 as Washington holds off San Diego 66-63
Jaylen Nowell scored 12 of his 18 points in the second half, Noah Dickerson added 16 points, and Washington held off a late rally to beat San Diego 66-63 on Monday night.
Parks expects to return for Memphis for visit to No. 22 LSU
Memphis first-year coach Penny Hardaway's team gets an early season opportunity to gauge itself when it visits No. 22 LSU on Tuesday night in its first road game.