Jones' shot made it 55-53 and, after the Bulldogs suffered a turnover on the inbounds play, R.J. Scott hit a free throw with seventh-tenths of a second remaining.
Tevin Calhoun scored 12 points to lead the Trojans, while Jones and Hunter Williams added 10 each.
Jalen Steele's 16 points paced Mississippi State, which was making its debut under coach Rick Ray. Trivante Bloodman had 11 points and Gavin Ware 10.
Steele hit two free throws with 1:10 remaining to tie it 53-53. Mississippi State rallied from an eight-point deficit with 8 1/2 minutes to play.
Troy led by as many at 16 points in the first half. It was Troy's first game in the $40 million Trojan Arena.