Will Barton added 10 points as the Tigers (9-5) used a strong inside game from Black, complemented by Antonio Barton connecting on 5 of 7 from the field, including 4 of 5 outside the arc.
Barton, who did not start after being late for a team meeting, finished 4 of 13 from the field. Black grabbed seven rebounds, helping Memphis outrebound Tennessee 36-26.
Trae Golden led Tennessee (7-7) with 22 points, connecting on 8 of 14 from the field.
The win was the second for Memphis over Tennessee this season. The Tigers won 99-97 in double overtime Nov. 22 at the Maui Classic.
Washpun and Will Barton were both assessed technical fouls, but there were no ejections.
Memphis would use a 16-4 rally midway through the second half to turn a 10-point advantage into a 65-43 lead with 2:46 left.
Memphis benefited from an offense that relied on passes to the rim resulting in dunks. That helped Memphis carry a 28-20 lead into the halftime.
No Memphis player was in double figures. Golden led the Volunteers with 10 points, hitting 4 of his 8 shots in the half. The rest of the Tennessee players were a combined 5 of 22.
Memphis used the dunks to shoot 40.7 percent (11 of 27) for the half. Both teams were 2 of 10 from 3-point range.
The first half was close before a dunk by Black was followed by a 3-pointer from Chris Crawford to give Tigers a 22-15 lead with 5:21 left in the half.
Golden connected on consecutive 3-pointers for Tennessee, but Memphis was able to hold onto its lead at the break.
The Memphis lead would finally reach double digits on a 3-pointer by Antonio Barton, and would stretch to 44-32 as he connected on a trio of free throws.
The Tigers would continue to build the lead as Tennessee continued to shoot poorly, ending the night at 36.2 percent (21 of 58), including 5 of 21 from outside the arc (23.8 percent). Skylar McBee, who had connected on at least three 3-pointers in five of the last six games, was scoreless, including missing all five of his long-range shots.
Nike Men's Tennessee Volunteers Tennessee Orange ELITE Shooter Long Sleeve ShirtShop
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.