The score was tied at 55-all with just under 13 minutes to play when Hamilton made a layup and back-to-back 3-pointers to spark an 18-6 run that put the Phoenix up by 10 points with 8:22 left on the clock.
The Blue Hens (4-15, 3-5 Colonial Athletic Association) then scored seven straight points to cut the difference to three. Elon (11-10, 3-5) outscored Delaware 23-14 down the stretch - making 4 of 4 from long range - to stay in front.
Kevin Blake scored 19 points for Elon, Tanner Samson had 12 with 10 rebounds, and Christian Hairston and Elijah Bryant each finished with 10 points. Hamilton shot 10 of 13 from the floor and made six 3-pointers.
Kyle Anderson led Delaware with 25 points.