Chris Warren added 18 points for Ole Miss (8-2), which recorded its fifth straight win. Warren shot 3 of 13 from the field and 12 of 12 from the free-throw line.
The Rebels hit 25 of 29 from the line (86.2 percent), including 16 of 18 in the second half and 10 of 10 in the final 3:29, when they led 71-64.
The Bobcats (2-8) hit 2 of 5 foul shots after the break.
Ole Miss jumped out to a 12-0 lead, but Texas State tied the score seven times before a 6-0 spurt gave the Rebels a 40-35 halftime lead.
"I thought we came out great, but we got up and put it in cruise control," Rebel head coach Andy Kennedy said. "We had guys fouling, not as aware as we needed to be. It's a good lesson, and we'll take something from it. We take no game for granted."
Ole Miss led by as many as 13 in the second half. Terrance Henry finished with 13 points and Reginald Buckner had 13 rebounds.
Eddie Rios and Cameron Johnson scored 16 points apiece for the Bobcats, who have lost seven in a row.