Bembry finished with 14 points, 13 rebounds, nine assists and three steals of the Hawks' 10 steals.
Jordan Price scored 17, including four 3-pointers, for the Explorers (15-15, 7-10 Atlantic 10), who had 12 assists on 17 field goals, but shot just 31.5 percent.
Bembry and James Demery combined to score 10-straight points, giving St. Joe's (13-16, 7-10) a 49-42 lead with 3:44 remaining.
Price scored six-straight points to pull La Salle within one, but Wilson hit a 3-pointer with 39 seconds to play and then 1 of 2 free throws 13 seconds later to make it 53-48.
A layup by Price made it a one-possession game, but Bembry's free throws with five seconds left sealed it.