Eaves made 7 of 12 field goals and 14 of 16 free throws while Stephens hit 7 of 8 shots. Daryll Palmer finished with 11 points and eight rebounds for South Carolina State (3-3).
The Bulldogs took a one-point lead into halftime and Ivory Drummer's 3-pointer gave Allen a 62-52 advantage with 13 minutes to play, but a 3 by Stephens sparked a 10-1 run that cut South Carolina State's deficit to one.
Drummer made a layup to put Allen up 73-70 with 4:36 remaining, but Eaves scored seven in a row, and 12 during a 15-1 run, to close the game.
Drummer led Allen with 20 points and nine rebounds.