Derrick Millinghaus made a free throw before the Rebels got the ball back after a shot-clock violation. Millinghaus hit a layup with 44 seconds left to cut A&M’s lead to 67-65.
Turner then hit a jump shot from the corner with 16 seconds left to extend the lead.
Millinghaus made two more free throws with 10 seconds remaining, and the Rebels had to foul three consecutive times to get into the bonus. Star Marshall Henderson fouled out on the last foul in that span.
Turner missed his free throw with 5 seconds left, but Millinghaus, a freshman, missed a shot at the buzzer to give A&M (15-9, 5-6 SEC) the win.
Mississippi (18-6, 7-4) has dropped four of its last five games after opening SEC play 6-0.
Texas A&M held Henderson, who entered the game leading the SEC in scoring with 19.9 points a game, to 10 points. Millinghaus and Reginald Buckner scored 13 points each for Mississippi. Eight of the points by Millinghaus came in the last 4 minutes, and Buckner had 15 rebounds.
It was the most points for Turner since he scored a career-best 40 in a win at Kentucky last month. He set a record for most points at Reed Arena, outdoing the 36 Baylor’s Curtis Jerrells scored in a five-overtime win against A&M in 2008.
This was only the second meeting between these new conference foes, and the first since an A&M win on Dec. 30, 1972. The Rebels were playing in Texas for the first time since a trip to the NCAA round of 16 in San Antonio in 2001.
Turner bounced back from a terrible shooting performance in Saturday’s loss at Georgia, when he was just 2 of 14 from the floor.
Fabyon Harris added 13 points and had three steals for Texas A&M.
A 3-point play by Millinghaus got Mississippi within three points with just under 4 minutes left, but a layup by Kourtney Roberson pushed the lead to 67-62 a few seconds later. Mississippi had cut the lead to four points with a layup by Nick Williams before Harris scored four quick points to make it 65-57 with less than 6 minutes remaining.
Texas A&M trailed by one point before using a 6-2 run, with two 3-pointers by Turner in less than a minute, to take a 59-54 lead midway through the second half.
Mississippi led 38-35 at halftime, but Turner opened the second-half with a 3-pointer to tie it. The Aggies were down by two points a few minutes later after a dunk by Buckner before scoring five straight points to take a 49-46 lead, and they didn’t trail again.