Darden hit four 3-pointers while Jervon Pressley scored 15 points on 5-of-7 shooting for Hampton (1-2).
Lawrence Cooks hit a 3-pointer with 8:10 to play, capping a 9-0 run by Hampton and extending its lead to 64-43, its biggest of the game.
Alcorn State (0-3) responded with a 20-7 run, capped by a 3-pointer from Leantwan Luckett with 3:36 left to make it 71-63.
Hampton made 9 of 10 free throws from there to seal it. The Pirates were 23 of 26 from the stripe for the game.
Tyrel Hunt scored 17 and Marquis Vance added 16 points, eight rebounds and four assists for Alcorn State.
Hampton out-rebounded the Braves 40-30 and turned 15 offensive rebounds into 18 second-chance points.