Wright State (11-10, 3-4 Horizon) scored the first eight points of the game - including 3-pointers by Griffin and Chrishawn Hopkins - and rode that momentum to a 33-27 lead at intermission, though Detroit scored the final eight points of the half to make it that close.
The Titans trimmed the deficit to two on Chris Jenkins' 3-pointer when play resumed, but Wright State scored 12 of the next 14 points and Detroit trailed by double digits until 2:56 remained, as Anton Wilson cut it to nine with a 3-pointer at 56-47.
Griffin responded with a 3 of his own and the Raiders made 5 of 7 from the line down the stretch.
Grant Benzinger added 18 for Wright State.
Detroit (10-12, 3-4) was paced by Wilson with 15 points, including four 3-pointers.