Ty Green led the Spartans (8-4) with 25 points and Fred Miller added 15.
The Tigers, who trailed by five early, had a 14-0 run to go ahead 29-21. Woodson hit back-to-back 3's, then had three free throws before getting a steal that led to Powell's trey.
Powell had another 3 as the Tigers scored the last seven points of the half for a 42-29 lead.
Green had seven straight points to help SC Upstate get within 63-61 midway through the second half but a 13-1 run put Memphis back in control.
The Tigers shot 51 percent, including 11 of 21 on 3-pointers.