The Quakers used an 11-2 run to start the second half, opening up a 37-28 lead with 14:34 to play. Delaware State (0-2) slowly chipped away before taking its only lead of the second half, 52-51, when Devin Morgan completed a 3-point play with 2:57 left.
Howard made a layup and, after a Delaware State miss, Nelson-Henry hit another to put Penn up by 3.
The Hornets missed a 3-pointer before another Howard layup made it 57-52 with 41 seconds remaining and Penn hit 3 of 4 free throws from there to seal it.
DeAndre Haywood led Delaware State with 13 points while Morgan scored 12.