The visiting Tigers trailed by as many as 13 points in the second half, but made a 13-0 run to pull ahead in the second half. Auburn built the lead to as many as eight points, but went cold with its shooting down the stretch.
It took a three-point buzzer beater by Varez Ward to tie the game at 56-56 and send it into overtime. Prior to that shot the guard had missed 12 of his previous 13 threes this season.
LSU jumped to an early 10-2 lead as sophomore Ralston Turner hit a pair of threes. Auburn cut the lead to 15-11 on a three by Sullivan, but LSU went on a 9-3 run to build the lead into double figures.
The home team's largest first half advantage was at 28-15 on a basket by Storm Warren. At the half the Bayou Bengals led 34-27 after Sullivan launched a buzzer-beater from beyond the halfcourt line that sailed home for three points.
The Tigers cut the lead to 34-32 at the 17:14 mark as LSU called a timeout after Sullivan nailed a three and Josh Wallace stole and pass and scored on a fastbreak layup.
Rob Chubb tied the game on a left-handed hook shot with 16:54 to play and Sullivan's three from the corner with 15:31 put Auburn up 37-34, its first lead of the game.
Auburn build the lead to 46-38 on a layup by Josh Langford, but LSU tied the game at 46-46 with 7:54 left in regulation on a baseline turnaround shot by Storm Warren.
Neither team could pull away the rest of the second half. With the score tied at 53-53 Anthony Hickey picked up a deflected pass and threw in a three-point shot to put LSU on top with 21.4 seconds left.
Auburn got three shots to tie it as Kenny Gabriel and Frankie Sullivan missed on three-pointers. Rob Chubb rebounded Sullivan's shot that went in and out of basket, passed the ball to Ward whose trey with two-tenths of a second left tied the game.
However, after that the Tigers were able to score just two points in the five-minute overtime on a Chubb tip-in. That came with just under a minute to play to cut the lead to 61-58.
Auburn fell to 11-7 overall and 1-3 in the SEC while LSU?improved 12-6 overall and 2-2 in the league.
Sullivan led Auburn in scoring with 19 points while Chubb added a double-double, the first of his college career, with 15 points and 12 rebounds.
LSU held a huge shooting advantage, making 44.9 percent (26-59) of its field goals while Auburn hit 34.9 percent (22-63). LSU was 6-20 on threes, Auburn was 6-24.
LSU made 7-9 free throws, Auburn made 8-15 free throws. Chubb was the main offender at the line, making just 1-5, including two misses on the front end of one-and-ones.
Auburn finished with 13 turnovers while LSU had 10.
LSU's Anthony Hickey (left) and Chris Denson run to retrieve a loose ball.
"At the end of the day they made a few more plays than we did," Auburn coach Tony Barbee said. "I was proud of the way we fought back from that halftime deficit. We came out of the locker room and talked about those first four minutes really stepping out and stepping on them and we did. We got ourselves back in it."
Auburn held a 44-37 rebounding advantage and was plus 14 on the boards after halftime to spark the comeback. "It was good to see Rob Chubb come off a performance where he had no rebounds and step up tonight and have a double-double for us," Barbee said. "He played well in spots, but he also broke down in a couple of other spots.
"It is unfortunate because I thought we played well enough to win the game," Barbee said. "We are still searching for that guy we can go to late."
Starting Lineup: The Tigers opened the game with Chris Denson and Varez Ward at guard, Adrian Forbes and Kenny Gabriel at forward and Rob Chubb playing center.
At the Half: Auburn hit 9-23 field goals in the first half for 39.9 percent. The Tigers were 3-5 on three-pointers and 6-10 at the foul line. Sullivan led Auburn in the opening half with 13 points as he hit 3-4 treys.
LSU hit 14-29 field goals for 48.3 percent and 3-8 treys. The Bayou Bengals were 3-3 at the foul line while out-rebounding the Tigers 18-12. Hamilton led LSU in scoring at the break with nine points and five rebounds.
Offensive Drought: Gabriel struggled mightly with his shooting, making just 3-14 field goals and going 0-8 on threes. He did contribute on the boards with 10 rebounds.
Offensive Drought, Part 2: Ward also struggled with his shooting, making just 1-8 field goals. Like Gabriel, he contributed on the boards with nine rebounds.
Offensive Drought, Part 3: Denson did not score and was 0-5 on field goals.
Up Next: Auburn takes on South Carolina on Saturday at the Auburn Arena. Tipoff is set for 12:47 p.m. CST.