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.