The Tribe (6-1, 4-1 Colonial Athletic Association) trailed 13-3 after Delaware's Mike Perry made a 40-yard field goal on the final play of the first half.
Callahan went 7 of 10 for 93 yards for the Tribe, who have won six straight since losing their season opener to Massachusetts. The Blue Hens (7-1, 4-1) pushed their lead to 16-10 on Perry's 20-yard field goal early in the fourth, until Grimes' touchdown pass to Hill put William & Mary ahead for good.
Hill caught six passes for 92 yards. Grimes rushed for 77 yards.