Seemingly in control for most of the game, LSU (16-6, 8-1 in the Southeastern Conference) saw a 72-58 lead with 5:16 left disappear into a 77-75 deficit in the final minute.
But with LSU out of timeouts, Mitchell (27 points) rose above Charles Thomas' defense to bury a big shot from the top of the key for a 78-77 Tigers lead.
Ronnie Brewer, who had spearheaded Arkansas' comeback with 24 points, raced back up the floor and did well to split two LSU defenders, but his 17-foot leaner hit the back iron as 7,668 fans in the Maravich Assembly Center celebrated.
Hogs coach Stan Heath had called his last timeout with 28.9 seconds left and inserted freshman Sean McCurdy for more quickness, never anticipating that LSU would foul McCurdy.
"We thought they would foul either Thomas or Brewer right away," Heath said.
Instead, Brewer saw a 3-on-1 fast break opportunity developing and passed ahead to McCurdy, who was fouled and missed two free throws with 24.4 seconds left and Arkansas leading 77-75.
"There's a great kid who works his butt off," Heath said. "You watch -- he'll be fully prepared for that situation down the road."
Hogs assistant Ronny Thompson put a consoling arm around McCurdy after the game.
Brewer defended McCurdy and said, "I thought we had a great effort and came together as a team. We were down so many points but we kept digging and playing hard."
As devastating as this defeat was for Arkansas (15-7, 4-5 in the SEC), Heath agreed with Brewer.
"No question," Heath said. "We put our heart out there. It's refreshing to know what kind of guys were in our locker room."
Brewer said Mitchell made "an incredible shot."
But with all the back-and-forth drama at the end, the story was written inside, where LSU outscored Arkansas 46-28 in the paint and outrebounded the Razorbacks 39-32.
Glen Davis, playing with passion and joy, had 19 points and 16 rebounds for the Tigers.
Tyrus Thomas added 11 points and 6 rebounds, and helped Garrett Temple defend Brewer's final shot of the game, forcing him to dip underneath just to get the ball off.
"College basketball is something, isn't it?" said LSU coach John Brady. "I don't think we played real smart down the stretch. But I remember Nick Saban saying this when he was our football coach -- the main thing is LSU won."
Brady wasn't so happy at halftime, when LSU led 39-33 and Brady felt Arkansas' Jonathon Modica had fouled Mitchell on the final 3-point attempt of the half.
Brady stormed toward the media table, where SEC supervisor of officials Gerald Budreaux sat next to former Mississippi State coach Richard Williams.
"What was that, Richard?" Brady asked Williams.
"I thought he hit him," Williams said.
"That's what I thought," Brady said.
Later, Williams, for whom Brady once toiled as an assistant, joked, "I should have said to him, 'Why are you asking my opinion? You never cared about it before.' But he would have choked all of us."
After Arkansas shot nine free throws to LSU's one in the first half, the first six fouls in the second half were called against Arkansas. Still, for the game, Arkansas made 17 of 22 free throws to LSU's 5 of 11.
Williams, who had interviewed Heath on Tuesday night for a TV show, said about the game's final moments, "That's a shame. Arkansas really needed this road win, and Stan coached his butt off. He called a good timeout at the end. There was nothing he could do about the way the game ended."
Brewer said about the final few seconds, "Coach said he wanted me with the ball in my hands at the end. I tried to get separation, pump-faked and stepped through to get an open look. Unfortunately, it didn't fall for us."
Heath said, "I've never experienced anything like this, where games have gone south on us in different ways. But I know these guys are going to keep on fighting."
Modica scored 13 of his 20 points in the first half, continuing his offensive improvement. Arkansas forwards Thomas and Darian Townes each scored 10 points off the bench for the Hogs, after freshman Cyrus McGowan started.
LSU shot 53.2 percent to Arkansas' 44.3 percent, but Brewer nearly made that moot by pouring in 13 points in the final 5:04.
"This loss really hurt us," Thomas said. "But we can't hang our head. I'm proud of the way we came back."
The Razorbacks now draw Auburn at home on Saturday night, as they try to return to .500 in the SEC.
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