The Wildcats (15-6, 6-2 Southeastern Conference) led by one point before Mays made two free throws with 15 seconds left. Texas A&M (13-8, 3-5) had a chance to tie it after that, but Elston Turner's 3-pointer bounced off the rim with 5 seconds left. Mays added another free throw with a second left to secure the win.
The Wildcats opened overtime with a 7-1 run thanks to a jump shot by Noel and five free throws to take a 69-63 lead.
Turner's 3-pointer with about 2 minutes left in overtime got A&M within 69-66.
Kourtney Roberson's layup made it 69-68 with 16 seconds left before the free throws by Mays.
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Jalen Rose and David Jacoby announce their choices for sleepers in the 2016 NBA Draft.
Daryl Gross, who spent a decade as Syracuse's athletic director, will start as Division II Cal State-Los Angeles' AD in July.
Utah forward Brekkott Chapman, who averaged 4.4 points and 2.8 rebounds last season, has transferred to Weber State, coach Randy Rahe announced Wednesday.