It was Auburn's eighth win in nine games.
"It was a very special moment," Barber said. "We went out with a bang like everybody wanted us to."
Barber finished with 16 points and 17 rebounds as Auburn (21-10, 10-6 Southeastern Conference) scored 42 points in the paint and outrebounded the regular-season champions 45-37.
The win capped Auburn's best regular season since 2003. Barber said he and the other veterans have remained patient knowing the wins would come eventually.
"We just kept working, stayed focused and everybody stayed together. When you're losing, it's real hard to stay together, but we found a way to stay together as a team and it paid off in the end," said Barber, who had 13 points and 10 rebounds in the first half.
Auburn coach Jeff Lebo called Barber's performance amazing.
"He was unbelievable and incredibly active off of the glass," Lebo said. "He was all over the glass with his quickness."
Marcus Thornton had 23 points for LSU (25-6, 13-3), which lost its second straight and posted its lowest point total of the season.
Rasheem Barrett had 12 points for Auburn and DeWayne Reed added 11.
Lebo credited his team's defense for the victory.
"Defensively is where we were really solid. We spent a lot of time in preparation," Lebo said. "They're a very, very physical team and I thought Vot (Barber) was terrific, because he spent the majority of the time on Mitchell."
Lebo was referring to LSU's Tasmin Mitchell, who entered the game averaging 16.8 points, but was held to five by Auburn.
The Auburn players said they weren't going to worry about whether the win over LSU was enough to get the Tigers into the NCAA tournament.
"I really don't focus on what these people say about the brackets and things like that," Quantez Robertson said. "We can't worry about what the writers say about the NCAA tournament."
Barrett made two free throws with 6:31 left in the first to start a 10-2 run by Auburn, which went on to lead 34-28 at halftime.
Barber also had a layup and a dunk during the run that gave Auburn a 31-21 lead with 2:53 to play in the half.
Auburn finished the season as the only SEC team to beat both West Division champion LSU and East Division champion Tennessee.
The first half ended with a technical foul being called on LSU. Because the technical came after the first half had expired, the second half started with Tey Waller hitting two free throws to give Auburn an eight-point lead.
LSU coach Trent Johnson said the technical was called because of the way he looked at referee Doug Sirmons.
"I've gotten three T's -- two for looking at somebody," Johnson said.
LSU could never get any closer as Auburn dominated the second half, stretching the lead to as many as 17 points.
LSU had cut the lead to 13 points and had the ball when Reed stole it from LSU's Terry Martin. Seconds later he was under the basket to take a pass from Barrett and for a layup that gave Auburn a 65-50 lead with 3:37 to play.
LSU could get no closer than 14 after that and both teams played mostly substitutes in the final minutes.
Both teams earned first-round byes in the SEC tournament, which begins Thursday in Tampa, Fla.