Wallace and Sullivan are two of the team's five seniors, all of whom started — even walk-on Dylan Spencer, who scored the first points of his career with an early 3-poiner.
"I'm disappointed for them that we've had the kind of season we've had," Barbee said. "They deserve more. They deserve to go out as winners."
The Tigers shot 51 percent (28 of 55) and at one point led 44-38 early in the second half.
Tennessee attempted 38 free throws while Auburn was 10 of 12.
"I've never seen a stat sheet like these," Barbee said. "We had four more field goals, two more 3s and a team takes 23 more foul shots than you do. Never seen that before. That's the difference in the ball game."
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 a 14-2 run with a 3-pointer. McRae scored seven points to help the Vols take a commanding 77-64 lead into the final minutes.
Auburn cut it down to five after a pair of Noel Johnson 3-pointers in the final 1:15 but got no closer. Josh Richardson and Golden each hit a pair of free throws after that.
Vols coach Cuonzo Martin even said he wasn't surprised that it was closer than many expected.
"I even said to the guys before the game started that it would go down to the wire because of what's at stake," Martin said. "Those guys played with emotion. I read in the paper that Frankie Sullivan said he didn't want to lose this game. We knew that."
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 against Georgia.
McRae has suffered no such lapse. He 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. Wallace made 5 of 7 shots and had four assists.
"He gave everything he could to win this game," Barbee said.