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.