Tulane outscored Southern (1-5) by 11 points from the free-throw line.
The Green Wave (4-2) led 14-1 early in the first half and 34-21 at the break. The advantage grew to 50-33 on Tarrant's 3-pointer 6:06 into the second half, but the Jaguars' 14-3 run made it 53-47 on Tarrant's free throws with 8:55 to go, and Southern kept chipping away.
Southern closed to 66-63 on Miller's 3-pointer with 30 seconds left and 67-65 on Grace's layup with 15 seconds remaining, but Kendall Timmons made 1 of 2 free throws, and Beltran missed a 3-pointer with 3 seconds to go.
While the Wolverines had some turnover to their roster, they still could have a leg up in a conference that lost a lot of star power.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.