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.
The recruiting landscape is heating up. Find out where the top 30 players in the 2019 ESPN 100 are headed next season.
James is the highest-ranked prospect to commit to the Vols under Rick Barnes and the highest overall since Tobias Harris in 2010.
Five-star point guard Josiah James, ranked No. 20 in the ESPN 100, has committed to Tennessee over Clemson, Duke and Michigan State.