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.