Mercer became one of three teams seeded either last or next-to-last in their quarter of the draw to advance to the tournament's second round -- joining Robert Morris and Stony Brook.
Mercer (24-11) won the Atlantic Sun regular-season title, but the conference's tournament was captured by Florida Gulf Coast.
The Bears made 50 percent of their field goal attempts against the Volunteers with Langston Hall scoring 16 points and Daniel Coursey adding 15.
Mercer will meet BYU in the second round after the Cougars eliminated Washington on Tuesday.
Tennessee (20-13), which lost to Alabama in the quarterfinals of the Southeastern Conference tourney, was led by 20 points from Trae Golden.