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.
Temple men's basketball star during the 1950s Hal "King" Lear died on Saturday at his White Plains, New York home.
Sebastien Bellin's friend Chris Young joins Ryan Smith on Outside the Lines to discuss his friend's bravery, courage and strength after surviving the Brussels bombings in March.
Andrew White III is leaving the Nebraska men's basketball team and will play elsewhere for his final college season.