The Volunteers (15-7, 5-2 Southeastern Conference) won their fifth straight league game and controlled the game throughout even without injured leading scorer Scotty Hopson.
The Tigers (8-14, 1-7) couldn't follow up their first SEC win, at South Carolina, without suspended starting center Rob Chubb.
Williams had eight rebounds and Tatum seven as the Vols dominated the boards 38-24, allowing Auburn to grab just seven rebounds in the first half. Tobias Harris added 14 points.
Allen Payne led Auburn with 13 points and seven boards.
The Vols gradually turned a 13-point halftime lead into a 60-38 rout in the first 10:26 of the second half.
Auburn managed to whittle it down in the final minutes with an 18-9 finishing run after Tennessee had emptied its bench.
Auburn was the last SEC campus where Tennessee's coaching staff had never won.
Tennessee was better able to shake off a missing starter than the Tigers. Hopson didn't make the trip after spraining his left ankle in Tuesday's practice. Josh Bone, who started in Hopson's place, had eight points and three assists.
Chubb was suspended indefinitely for violating unspecified team rules, Auburn announced before the game. His sub, Adrian Forbes, wasn't as effective with one point and one rebound in 24 minutes.
With Josh Fields limited by early foul trouble, the 6-foot-10, 272-pound Williams had 12 points by halftime, five more than his season average coming into the game.
The Vols had 17 assists on 23 baskets and made 19 of 24 free throws. They have won their last three SEC games by a combined 52 points and five of their last six games overall.
Coach Bruce Pearl has only one more game left on his eight-game SEC suspension, but his team has gotten hot without him.
The Vols built a 37-24 halftime lead largely on Williams' inside play. He had 12 points and four offensive rebounds in the opening half.