Nieves scored nine straight points to cut a 34-24 Jackson State second-half lead to one point before a layup by Marius Myles gave the Braves (4-14, 2-1 Southwestern Athletic Conference) a 35-34 lead with 8:39 remaining.
LeAntwan Luckett's dunk with 1:05 left put Alcorn State ahead to stay, 49-48, in a game that featured 11 lead changes and eight ties.
Alcorn State has beaten the Tigers (1-11, 0-3) five straight times.
Jackson State led 28-18 at halftime after shooting 45.8 percent (11 of 24) to the Braves' 21.7 percent (5 of 23). Kelsey Howard scored 12 points for the Tigers during a 13-1 run that wiped out a 15-13 Alcorn State lead.
Howard and Jeff Stubbs finished with 12 points each for Jackson State.
ESPN college basketball reporter Andy Katz looks into the two decommitments from the NBA draft and what they're looking forward to.
With a trio a top recruits from Philadelphia, the Penn State basketball program is primed to finally turn a corner.
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