Tyrone Hanson added 10 points for the Tigers (9-9, 5-1 Southwestern Athletic Conference), who ended the game on a 22-9 run to rally from a six-point deficit.
Prairie View took its largest lead, 54-48, midway through the second half and was up 59-55 before Jackson State scored seven straight points. Rod Melvin hit two free throws with 5:36 remaining to give the Tigers a 60-59 advantage, and they led the rest of the way.
Jackson State took a 30-28 lead into intermission after leading by 10 in the first half.
SMU has signed a second player from Australia, 6-foot-11 forward Harry Froling, to a national letter of intent. The Mustangs previously signed guard Tom Wilson from Australia.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.