All-SEC senior Alli Smalley had a chance to send the game into overtime, but her baseline jumper to beat the final buzzer hit the rim.
The Tigers wasted a career-high scoring effort from junior forward Chantel Hilliard, who contributed 18 points and led the Tigers on the boards with 11 rebounds.
Chantel Hilliard (with ball) picked up the scoring slack with Blanche Alverson being held scoreless.
With the loss the Tigers dropped to 15-15 and Mississippi State improved its record to 13-16.
Auburn came into the tournament as the sixth seed while Mississippi State was seeded 11th. The Bulldogs advance to a Friday night game vs. No. 3 seed Vanderbilt.
Smalley scored 14 points for the Tigers, but Auburn's all-time leading three-pointer shooter did not make a trey nor did any of her teammates. The Tigers were 0-8 on threes while the Bulldogs made 6-20.
The Tigers also hurt their cause at the foul line. Auburn made just 7-16 free throws while Mississippi State hit 7-10.
Auburn out-rebounded MSU 40-35 and had 15 turnovers, four fewer than Mississippi State.
Both teams struggled to score early in the game. The Tigers didn't get on the scoreboard until 13:38 remained in the half when Parrisha Simmons hit a free throw. However, Auburn trailed just 2-1 because MSU couldn't find the range on its shots either.
By halftime the Tigers managed to build a 22-15 lead despite going 0-5 on threes and 4-8 free throws while making 9-30 field goals.
Mississippi State hit 7-25 field goals, 1-8 threes and did not take a foul shot.
Auburn built its halftime lead by outscoring the Bulldogs 14-4 on second chance points.
Midway through the second half the Tigers built the lead into double figures as Hilliard made back-to-back baskets inside to make the score 39-28 with 10:29 to play, but the Tigers could only score eight more points after that.
"Mississippi State out and executed a lot better than we did," Smalley said. "We had a lot of breakdowns defensively. We didn't play with the energy we needed to win a game in the SEC Tournament."
Auburn coach Nell Fortner said Auburn's lack of success at the foul line cost the Tigers a chance to advance to Friday's game.
"I am disappointed in the loss, especially when you have a great senior like Alli Smalley, but you have to give Mississippi State credit," Fortner said. "They played very hard and never backed down."
MISSISSIPPI STATE (49)
Diamber Johnson 6-16 2-4 16; Mary Kathryn Govero 5-12 3-4 15; Catina Bett 4-6 2-2 10; Porsha Porter 1-10 0-0 3; Danielle Rector 1-1 0-0 3; Ashley Brown 1-5 0-0 2; Darriel Gaynor 0-0 0-0 0. Totals 18-50 7-10 49.
Hilliard, Chantel 8-15 2-5 18; Smalley, Alli 7-18 0-0 14; Simmons, Parrisha 2-3 2-3 6; Tanner, Tyrese 1-6 2-6 4; Davis, Peyton 1-1 0-0 2; Williams, Jassany 1-6 0-0 2; Jennings, Morgan 0-4 1-2 1; Alverson, Blanche 0-5 0-0 0; Strain, Courtney 0-0 0-0 0. Totals 20-58 7-16 47.
Miss. State 15 34 49
Auburn 22 25 47
3-point goals--MISSISSIPPI STATE 6-20 (Mary Kathryn Govero 2-6; Diamber Johnson 2-7; Porsha Porter 1-6; Danielle Rector 1-1), AUBURN 0-8 (; Smalley, Alli 0-6; Alverson, Blanche 0-2).
Fouled out--MISSISSIPPI STATE-Ashley Brown, AUBURN-None.
Rebounds--MISSISSIPPI STATE 35 (Ashley Brown 9), AUBURN 40 (Hilliard, Chantel 11).
Assists--MISSISSIPPI STATE 8 (Mary Kathryn Govero 3; Diamber Johnson 3), AUBURN 11 (Jennings, Morgan 3; Simmons, Parrisha 3).
Total fouls--MISSISSIPPI STATE 14, AUBURN 16.
Technical fouls--MISSISSIPPI STATE-None, AUBURN-None.