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.
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