In a first-place Southwestern Athletic Conference showdown, Joyner led the Delta Devils (8-11, 7-0) with 18 points, and Brent Arrington added 17. Crosby had 15 points and 12 rebounds.
Gibbs' driving layup at the regulation buzzer tied the score at 63-all.
In overtime, Joyner provided the first score with a 3-pointer, and Crosby had a three-point play to give the Delta Devils a 71-65 lead with 2:06 remaining. Joyner added a jumper, and Mississippi Valley State protected the lead at the free-throw line.
William Pugh scored 12 points for the Delta Devils.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.