Texas A&M (13-7, 3-4 Southeastern Conference) trailed by 14 points early in the second half but recovered to snap a four-game losing streak. Harris made 8 of 13 shots from the field and Turner sank a crucial fadeaway jumper with 30 seconds remaining in overtime to give the Aggies a 53-49 lead.
J'Mychal Reese scored 10 points, including four in overtime.
Mississippi State's Craig Sword banked in a 3-pointer with 5.9 seconds left to tie the game at 47 and send it into overtime. Gavin Ware led the Bulldogs (7-12, 2-5) with 14 points while Colin Borchert added 10. The Bulldogs have lost five straight.
Texas A&M started the SEC schedule with impressive back-to-back wins over Arkansas and Kentucky, but since then the offense has disappeared. It wasn't much better against the Bulldogs, but some big shots by Reese and Turner in overtime were enough to give the Aggies the win.
Mississippi State coach Rick Ray has preached a deliberate approach during his first season - especially because the roster has just seven healthy scholarship players - so the Bulldogs' 29-17 halftime advantage was nearly perfection.
Mississippi State was very efficient on offense, making 10 of 15 (66.7 percent) shots from the field, including 4 of 7 from 3-point range, and the defense forced 13 Texas A&M turnovers.
But the Bulldogs had trouble taking care of the ball in the second half with 14 turnovers. Texas A&M turned many of those into easy buckets and owned a 14-0 advantage in fast-break points.
The Bulldogs pushed their lead to 31-17 early in the second half but Texas A&M then started a methodical comeback, which resulted in a 16-2 run that tied the game at 33 with 13:30 remaining.
The teams traded blows until Texas A&M was finally able to create some separation when Turner hit back-to-back baskets to push the Aggies ahead 45-42 with 3:54 remaining.
But Mississippi State had one more run remaining and Sword's 3-pointer off the glass tied it at 47. Borchert's jumper pushed the Bulldogs ahead 49-47 at the start of overtime, but they didn't score another point during the final four minutes.
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