Howard's layup put Jackson State up 42-38 with 10:55 remaining and after Jordan Berry gave the Tigers a 48-43 lead with just less than six minutes left, Howard added another 3 to make it 51-45 three minutes later.
On UAPB's final possession, Martaveous McKnight took an inbounds pass at midcourt but his contested last-second heave bounced off the front of the rim.
Maurice Rivers chipped in eight points and nine rebounds for Jackson State (12-17, 9-7 Southwestern Athletic Conference). Collins, Howard and Rivers combined to grab all but six of the Tigers' 37 rebounds, while Collins had four -- and Rivers three -- of JSU's 10 steals.
Travon Harper led UAPB (11-20, 11-6) with 10 points and nine rebounds.
Mannion, who recently reclassified and is ESPN's No.11 overall player in the class of 2019, chose Arizona over Marquette.
He'll fit in with Sean Miller's plans for a faster tempo on offense.
Top recruits are starting to take their official visits, meaning it's time to make some predictions about where they're leaning.