The Mocs led by as many as 22 in the first half, and were ahead 38-28 at halftime, but saw the lead shrink.
Jordan Strawberry hit a 3-pointer that pulled Mercer (11-4, 1-1) to within 58-56, capping a single-handed 7-0 run and prompting a Mocs' timeout with 3:39 remaining.
Strawberry scored two from the foul line, keeping the Bears within 60-58, but Pryor hit a contested 3, and Tuoyo blocked Desmond Ringer's shot at the other end.
Strawberry led Mercer with 24 points, Jestin Lewis added 15.
With three blocks, Tuoyo became Chattanooga's career leader with 135.