They joined Florida and Kentucky in the round of 16 — the first time three SEC teams made it that far since 2007.
Tennessee will face second-seeded Michigan (27-8) in a Midwest Regional semifinal Friday night in Indianapolis.
Stokes broke his 2-day-old school tournament record for rebounds.
Langston Hall had 15 points to lead the 14th-seeded Bears (27-9). They knocked off Duke in the signature upset of the tournament but couldn't answer Tennessee's size.
Mercer trailed by double figures for the entire second half before the Bears threatened to give themselves yet another fantastic finish.
They had the ball down 12 with about 2 1/2 minutes left when Jakob Gollon — one of the heroes of the Duke upset two days earlier — threw the ball away in the lane, then fouled out a few seconds later.
Jordan McRae hit two free throws, and Richardson added a fast-break layup to push the Tennessee lead to 77-61 with 1 1/2 minutes left.
McRae finished with 13 points for the Volunteers, who have won eight of nine with the only loss coming to the top-ranked Gators in the SEC tournament.
They are in the round of 16 for the fourth time in eight years, and the third team to go from the First Four to the Sweet 16 since the introduction of the extra round in 2011.
They also got a bit of payback: Mercer ended Tennessee's season last year with a 75-67 win in the first round of the NIT.
Ike Nwamu scored 12 points, Anthony White Jr. had 11 and Daniel Coursey added 10 for Mercer, the plucky Atlantic Sun Conference school trying to match Florida Gulf Coast's run last year to the regional semifinals.
The Bears drew a perfect matchup for their first game — and couldn't have had a worse one for their second.
They were bigger, more experienced and more precise than a Duke team loaded with high school All-Americans and a leaky defense, carving them up down the stretch in a 78-71 victory that ranks among the top upsets in the history of the tournament.
Mercer starts five seniors and has seven on the roster — but the Bears were down one with 6-foot-11 Monty Brown out with a possible concussion.
Even with him, a Tennessee team with Stokes — who set the school's short-lived NCAA tournament record with 14 rebounds in an 86-67 rout of Massachusetts — was going to be a challenge.
Without him, it was nearly impossible.
Tennessee never trailed and held a 24-4 rebounding advantage in the first half. Richardson scored 10 straight points midway for the Volunteers to turn a tight game into a double-figure lead. His 3 from the right wing made it 29-18 with 6 1/2 minutes left.
Meanwhile, Stokes and Maymon effectively turned Mercer into a jump-shooting team: The Bears managed just one offensive rebound in the first half and didn't attempt their first free throw until there was just 8:40 left.