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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.