The Tigers fell to 3-7 in the SEC and 12-13 overall. The Bulldogs improved to 18-7 overall and 6-4 in the conference.
Lucas Hargrove posted a double-double for the Tigers. He scored 20 points and pulled down 10 rebounds as he hit 7-16 field goals.
Tay Waller, who made 5-11 threes, led the Tigers in scoring with 21 points and the guard added seven rebounds.
Dee Bost rallied the Bulldogs in the first half from a double digits deficit and hit key buckets down the stretch as he broke out of a lengthy shooting slump with a career-best 32 points. He made 11-19 field goals and hit 7-12 threes and pulled down nine rebounds.
Auburn hit 29-79 field goals for 36.7 percent while the Bulldogs made 29-70 for 41.4 percent. Auburn hit 9-33 threes while State made 11-34.
The Tigers out-rebonded the Bulldogs 47-46 and each time had just eight turnovers.
Mississippi State made 16-23 foul shots while Auburn hit 8-12.
"It is just frustrating," Lebo said of his team's loss. "I feel for the kids and the coaching staff. We did everything and had it right there for us again and just couldn't finish it out with some plays.
"Bost was terrific in this game," Lebo added. "We got really hurt at the point guard position. Bost had 32 tonight. (DeWayne) Reed really struggled tonight. He was 5-21 (field goals) and 1-8 (threes). He (Bost) was the guy who kept them in the game the entire game.
"We showed the character and toughness to be right there. It just hurt, two in a row on the road in overtime," Lebo added. "We were right there, up at the end. We just couldn't a couple of plays at the end."
Neither team took control of the game early in the first half. Auburn was the first team to make a run. With the score tied at 13-13, the Tigers scored 10 uncontested points after a steal and stuff by Hargrove. That prompted the Bulldogs to call a timeout with 12:34 left in the half.
The Tigers built the lead to 14 points at the 9:01 mark as Waller hit a three to make the score 31-17. However, by halftime the margin was down to 38-35.
The Bulldogs took the lead on a three by Bost to make the score 45-44 with 14:52. The Bulldogs built the edge to 51-44, but Auburn recovered and pulled ahead 55-54 on a fastbreak basket by Brendon Knox with 8:33 left.
The game was tight the rest of the period. Auburn increased its lead to four with Waller hitting a trey with 3:16 left.
Mississippi State pulled ahead 74-72 with 30 seconds left on a fastbreak dunk and a free throw by Romero Osbey that sent Lebo into a tirade. Knox, who was called for a foul on the play, did not appear to touch the shooter.
Reed then scored to tie the game at 74-74. He was hit on his layup, but no foul was called. Auburn then got the ball back with 2.1 seconds left on a turnover as Hargrove grabbed the ball after a good defensive play on Bost by Sullivan.
The Tigers called timeout to set up a play. Frankie Sullivan was pushed in the backcourt as he shot the basketball, but no foul was called and the game went into overtime.
"I can't wait to look at the film on the end on the foul and the and-one on the dunk," Lebo said. "Frankie, I thought he got hit. I think any other time of the game they probably would have called that a foul, but you are not going to get it on the road. It was just a frustrating thing and they got to the foul line twice as much as we did."
The home team controlled the action after that with Varnado breaking the ice in overtime at the 2:02 mark with a hook shot to put the Bulldogs up for good with 2:02 to play. Bost then iced the game with a layup and a three-point basket. The Tigers were 0-9 from the field in overtime. Their only point came on a free throw by Johnnie Lett.
The Tigers will return to action at 6 p.m. CST at Florida.