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.