Auburn connected on just 39.1 percent of its shots and trailed 73-66 with just a little more than a minute to play. The situation looked bleak.
However, the Tigers refused to give up and started the comeback as Tay Waller drilled a long-range three in transition with one minute and six seconds left.
Baylor's Curtis Jerrell missed a three-point shot under pressure defense by the Tigers and Auburn got the ball back with 29 seconds to play.
Barrett then made a loud crowd even louder as he hit a three-pointer off a pass by Waller with 19 seconds to play.
Baylor had to in-bounds on the baseline after a timeout and on the first two tries the Tigers deflected the ball out of bounds. On the third try, the Tigers trapped Henry Dugat in the corner and Quantez Robertson forced a forced a turnover with 15.8 seconds to play.
Junior point guard DeWayne Reed took the ball and drove to the basket and took a hard foul. With 8.5 seconds left he missed both of his foul shots (he was 1-5 for the game at the foul line) and Baylor's Jerrells got the ball and was fouled with 6.9 seconds left, but made just one of two shots.
Robertson got the rebound and quickly got the ball up court. Barrett got a clean look for a three, but the shot was just barely long, ending the season for the Tigers and the college career of Barrett and fellow seniors Robertson and Korvotney Barber.
Barber scored 11 points and added 13 rebounds. Barrett led the Tigers with 16 points and Reed added 13.
Barrett said he didn't have time to be picky about his shot, but thought the do-or-die jumper had a chance. "I had a wide open look," he said. "It just hit the back of the rim."
Reed, a junior, said he felt bad about missing the free throws. "We wanted to go out with a bang with our seniors and we wanted to keep it going for the seniors. I missed two free throws and I know I hurt my teammates, but I know they're going to stick with me. The seniors did a good job of helping us come together as a team and I am going to miss them a lot."
Auburn coach Jeff Lebo said he was impressed by Bears. "Congratulations to Baylor, they are certainly deserving of a win. They are playing awfully well. It hurts obviously. We battled awfully hard. We had a chance at the end, a couple chances at the end, we just couldn't finish it off."
Lebo also had high praise for his team. "You could see in the grit and determination of the last two minutes of the game and see what kind of kids we have...what kind of makeup we have.
"Like I said before, we are kinda of like junkyard dogs. We keep playing, keep playing, we keep battling. We didn't shoot the ball particularly well tonight, but we still had a chance to win the basketball game and we just competed to the end."
Auburn finished its season with a 24-12 record. Baylor improved to 23-14.
"I am really proud of our seniors--Vot, Tez, Rasheem and Drew Smith," Lebo said. "They have had an unbelievable year. I am really proud of them for what they have accomplished."
Barber said he appreciated the support of the crowd that was into the game from start to finish. The paid attendance was 6,682 and there were considerably more people in the old coliseum making noise.
"It felt real good," he said of the support. "It was really our last game here at Beard-Eaves as seniors. I thank them for the support they brought tonight. They were behind us 100 percent. Unfortunately, we couldn't come out with the victory.
"We lost to a very talented team and I wish them the best on down the road," Barber added.
The lead changed hands early in the game before the Bears made the first run turning an 8-5 deficit into a 17-10 lead after Lacedarius Dunn hit a three at the 13:03 mark following a turnover by Frankie Sullivan.
The Bears built the lead to 22-12 on a basket by Dunn before Auburn went on a 10-0 run to tie the game that featured back-to-back threes by Reed and Waller.
DeWayne Reed drives in traffic.
At the break the Bears led 37-36 as they hit an even 50 percent from the field making 15-30 field goals. The Tigers also took 30 field and made 13 for 43.3 percent.
Auburn was 6-15 on threes in the first 20 minutes while Baylor made 4-10.
Baylor hit 3-4 free throws in the opening half while Auburn was 4-8 at the foul line.
Baylor held a 23-13 rebound advantage at the break. The Tigers had just six turnovers, three less than Baylor.
Barrett led the Tigers in scoring in the first half with 11 and Reed was next with 10.
Dunn led the Bears with 13 first half points.
The game was close the first 10 minutes of the first half with the score tied or Baylor leading by no more than four points.
Following a three from the week by Sullivan and a stuff by Barber on a good pass from Robertson, the Tigers got an open look for three by Sullivan to take the lead, but the freshman was off target.
The Bears then got a three from the corner by Dugat and a stuff by Mamadou Diene to take their lead to 59-53 prompting Lebo to take a timeout with 8:02 to play.
The Tigers managed to keep the game close to the final minutes setting up a memorable last minute, but not memorable enough to earn the Tigers a trip to next Tuesday's NIT semi-finals at Madison Square Garden in New York City.
"They hurt us with their penetration in the backcourt numerous times," Lebo said of the Baylor guards. "Jerrells is really good."
Jerrells scored 16 points, dished out eight asists and had just one turnover in 35 minutes. Dunn the Bears and all scorers with 19 points, Kevin Rogers scored 15 points and added a dozen rebounds while Tweety Carter scored 13 points and added five assists.
The Bears shot 50 percent for the game and made 7-19 threes plus 13-17 foul shots.
The foul line, a problem much of the year for the Tigers, helped end AU's season as the Tigers made 13-21 at the foul line. The Tigers were 9-27 on threes.
AU rebounded better in the second half and cut the Baylor margin to 39-35. Auburn had just eight turnovers, four fewer than the visitors from the Big 12.