Harrison's jumper with 28.2 seconds left boosted St. John's (9-5, 1-1 Big East) to its first win in three games.
JaKarr Sampson helped out with 16 points, eight boards and three steals in the Red Storm's triumph.
The Bearcats (13-2, 1-1), meanwhile, stumbled to their second loss in three games despite 23 points, 10 rebounds and four steals from Cashmere Wright.
Titus Rubles also hit double figures with 14 points for Cincinnati.
Celebrity Families of 2014 [PHOTOS]