James Madison led by just one point, 78-77, with two minutes left, but made 8 of 8 free throws in the final 34 second to seal it.
Tom Vodanovich had 17 points and grabbed eight rebounds for James Madison (13-9, 6-3 Colonial Athletic Association). Yohanny Dalembert added 17 points and Ron Curry had 15 points, seven rebounds and eight assists.
James Madison trailed 34-30 with 3:35 left in the first half, but Kent made back-to-back 3-pointers during a 10-0 run for a 40-34 lead at the break. Kent had 14 points at halftime.
Marvin King-Davis was 10 of 17 from the field and 11 of 13 from the line to total a career-best 31 points for Delaware (4-16, 3-6). Chivarsky Corbett and Devonne Pinkard had 12 points apiece.