Perry-Murray tied his career high with 13 points, on 5-of-5 shooting, and grabbed 10 rebounds. Ivy Smith Jr. made 8 of 10 free throws and finished with 15 points and Shirmane Thomas scored 13 for Grambling (5-12, 1/3 Southwestern Athletic Conference).
Thomas hit a jumper that gave the Tigers the lead for good, 58-57, and sparked a 16-4 run over the final seven minutes, 55 seconds. Dante Sterling made a 3-pointer that gave Alcorn State (4-13, 0-4) a 54-52 lead midway through the second half, but the Braves went 1 for 6 from the field and 6 for 10 from the free-throw line with five turnovers from there.
Sterling led Alcorn State with 14 points and Yalen Reed scored 12.
Grambling made just 24 of 60 from the field, including 3 of 12 from 3-point range, but grabbed a season-high 20 offensive rebounds and outscored the Braves 21-10 from the free-throw line.
James is the highest-ranked prospect to commit to the Vols under Rick Barnes and the highest overall since Tobias Harris in 2010.
Five-star point guard Josiah James, ranked No. 20 in the ESPN 100, has committed to Tennessee over Clemson, Duke and Michigan State.
Jim Calhoun, who has a career record of 873-380 and led UConn to three national titles before retiring in 2012, has been hired as coach at Saint Joseph.