Trying to keep their NCAA tournament hopes alive, the Volunteers (18-11, 10-7 Southeastern Conference) went on a 14-2 run in the final minutes after rallying from a six-point deficit early in the second half.
Tennessee rebounded after getting upset by Georgia to end a six-game winning streak and couldn't afford a loss to a team trying to avoid a last-place SEC finish.
Golden had 16 points in the second half and McRae remained one of the SEC's hottest players with 15.
Golden also had six assists and made all seven free throw attempts while committing just one turnover. McRae had seven rebounds and was 9 of 11 from the line.
Jarnell Stokes had 11 points and 12 rebounds for the Vols but made just one of 10 free throw attempts. The rest of the team was 26 of 28.
Frankie Sullivan broke out of a prolonged slump with 24 points before fouling out for Auburn (9-21, 3-14), which has lost eight straight and 14 of its last 15 games. It's the worst slump during a season for the Tigers since going 1-14 in 1942-43.
Josh Wallace added a season-high 14 points, 12 in the second half. The Tigers shot 51 percent (28 of 55) and at one point led 44-38 early in the second half.
No. 2 scorer Chris Denson didn't play for Auburn with back problems after trying to go during the shootaround.
Rob Chubb gave Auburn a 60-59 lead midway through the second half, then Skylar McBee started the decisive run with a 3-pointer. McRae scored seven points to help the Vols take a commanding 77-64 lead into the final minutes.
The Vols, who committed just eight turnovers, scored eight straight points after falling behind 44-38 early in the second half. Golden scored the first five points and McRae added a dunk and free throw.
Golden had a one-game struggle after averaging 18.7 points during the stretch, going 1-of-10 shooting and scoring just four points against Georgia.
McRae has suffered no such lapse. He came in averaging 26.8 points during his last five games and scored 35 against the Bulldogs.
The Tigers rallied from a nine-point deficit to take a 35-32 lead into halftime, largely thanks to Wallace's drives for baskets or fouls.
Auburn scored eight straight points and took a 35-30 lead on Brian Greene Jr.'s fast-break layup. Then Stokes missed two free throws but scored on a tap-in with 41 seconds left and the Tigers missed two 3-pointers on their final possession.