NASHVILLE, Tenn. — Ole Miss pushed Auburn hard, but not hard enough, at the Southeastern Conference men’s basketball tournament.

Auburn went on an 8-0 run in a little over a minute late in the second half to gain just enough separation to beat the Rebels 62-57 Friday in the quarterfinals.

Johni Broome finished with 23 points and 15 rebounds for Auburn. His basket with 11 seconds to go sealed the victory and sent the Tigers (28-4) to the semifinals against either Tennessee or Texas.

Sean Pedulla and Dre Davis led Ole Miss (22-11) with 12 points apiece. Malik Dia and Jaylen Murray scored 10 each. Ole Miss was just 4-for-23 (17.4 percent) from 3-point range.

“They’re the SEC champs. Projected 1-seed. You guys just saw it. What does that make Ole Miss? We can play with these teams. Disappointed locker room right now because we expected to win this game,” Ole Miss coach Chris Beard said. “I didn’t think we got beat, though. Like I told the guys, sometimes you win, sometimes you run out of time.”

The was tied at 46 when Auburn’s Chaney Johnson hit a 3-pointer with 6:05 left to give the Tigers the lead for good. Broome’s basket two minutes later made it 51-47, and he had another basket and a free throw to push it to 57-47 with exactly three minutes to go.

Ole Miss got back to within six, but missed a 3-pointer that would have made it a one-possession game with 1:45 left. Auburn saved two loose balls from going out of bounds off the rebound, which led to a fast-break dunk by Chad Baker-Mazara.

Ole Miss fought back again to cut it to 60-57 on Murray’s free throw with 38 seconds left. Then Broome hit a short hook shot from the left side as the shot and game clocks ticked down.

“Shot clock differential was just enough. We got a coach’s decision do we try to get one stop, we’re going to have about 10 seconds with the basketball, coming down with a broken floor, or do we extend the game by fouling?” Beard said. “Defense got better in the last seven or eight minutes of the game. We made the decision, players believed in it. What does Auburn do? Veteran team, well-coached, they get the ball to the right player in the right spot, and he made a tough shot.”

Ole Miss had another disappointing exit in the SEC Tournament. Since winning the tournament championship in 2013, Ole Miss has not been past the quarterfinals.

The good news for the Rebels is that they are expected to receive an at-large bid to the NCAA Tournament when the brackets are announced Sunday at 5 p.m. on CBS.

“We tell the players we want to be us. Why? Because us is pretty good. We’re one of the best teams in the country,” Beard said. “We’re going to get a nice seed, at-large bid in the tournament. Let’s not show up to the NCAA tournament and be somebody we’re not. Let’s be the best version of us.”

Beard added that, while the next week will be about the business of winning basketball games, he wants his players to enjoy and appreciate the NCAA Tournament experience.

“Secondly, we want to have some fun along the way. Yeah, it’s a business trip, no doubt about it. Man, you work your whole life in coaching and playing to play in the NCAA tournament, so let’s don’t forget that,” Beard said. “Let’s enjoy every practice, shoot-around, bus trip, the camaraderie, the hotels, the meals. You know this, man, the meals in the NCAA tournament are really, really good. Nobody even skips the salad portion of the meals because the salad looks like you’re at one of those Brazilian steakhouses.”