The Tigers (9-5, 1-0 SEC) have a clearer path to that goal now, thanks to freshman Tasmin Mitchell's 16 second-half points, freshman Tyrus Thomas' 13 points and 14 rebounds; and Glen Davis' late-game steal to go with 12 points and 10 rebounds.
Arkansas (11-4, 0-2 SEC), despite giving up a 30-6 LSU run in the middle of the game, had whittled a 44-32 deficit to 59-58 on Eric Ferguson's driving bank shot with 1:01 to play.
But Mitchell scored on one of Brady's six inbounds plays to put LSU up 61-58, and Heath had to call his last timeout with 15.5 seconds left when the Tigers double-teamed Darian Townes in the corner.
As Arkansas worked for the first good look, Davis read a Ferguson pass for Ronnie Brewer on the perimeter and stole it, pretty much sealing the win.
"In his whole career, Davis makes plays at the right time," said Arkansas assistant Ronny Thompson. "When his team needs a basket, a rebound or a stop, he gets it. He did it to us last year down there (in Baton Rouge, La.). He has fun with the game."
So much fun that afterwards, Davis slipped his head through the interview-room door and called out, "Great job, John Brady!"
Brady, who was holding court at the time, smiled and said, "He needs counseling."
When LSU won at West Virginia this season on the night Mountaineers great Jerry West had his jersey retired, Brady said Davis kept waving at West, who was sitting in the fifth row.
Arkansas, by contrast, seemed to tighten up after taking a 26-14 lead over the Tigers.
"We started so well, had great momentum and then just stalled," Heath said. "It became a bit mental. We've gotta be tougher."
The Hogs fell behind 32-31 by halftime, despite getting a 20-20 standoff in rebounds.
But LSU asserted its board strength in the final 20 minutes, finished with a 44-34 rebounding edge and also had just eight turnovers to Arkansas' 13.
Steven Hill, who had 4 points and 6 blocked shots for Arkansas despite missing 16 minutes of the first half in foul trouble, understands the urgency of the Hogs' task now.
"Vanderbilt beat Kentucky at Rupp (Tuesday night), so we've got to wear our hard hats (against Vandy) here Saturday. Every game is a must-win for us now."
A bit of good news for Arkansas was that Townes bounced back from a scoreless game against Mississippi State to get 14 points and 8 rebounds against LSU, but he missed two free throws and a couple of point-blank shots down the stretch.
Brewer led Arkansas with 16 points and 7 rebounds in 38 minutes.
Ferguson (10 points) was looking for Brewer for a possible game-tying 3-pointer in the late going, but LSU made good use of a switching defense.
"We just wanted a good look --a 3 or a 2," Thompson said.
Brewer said the same.
Hill said the Hogs would have liked a 3-point attempt, with time for an offensive rebound.
Heath said Arkansas wanted a shot by either Brewer, Ferguson or Jonathon Modica (seven points).
Davis missed a one-and-one with 6.5 ticks left, but LSU fouled Dontell Jefferson before Arkansas could try a potential tying 3. Jefferson missed his one-and-one before he could miss the second shot on purpose
Tasmin Mitchell's two free throws at 2.0 made things official.
"I thought our team did a great job, down 12 points, to hold their composure," Brady said. "I thought we could score if we executed. I thought we defended well the whole game, with two freshmen (Tasmin Mitchell, Garrett Temple) on Brewer and Modica."
Townes said Mitchell in particular played with a lot of confidence.
"We've got 14 games left and we can't let this affect us," Townes said.
Heath commended the play of Arkansas freshmen Cyrus McGowan (thunder slam follow) and Sean McCurdy (4 assists, 3 points in 10 minutes).
"Sean was very solid out there," Heath said. "He played with a lot of poise and toughness."
A season's-best crowd of 18,689 in Bud Walton Arena couldn't quite get Arkansas over the hump, as LSU twice narrowly beat the shot clock for baskets and Arkansas missed close shots at pivotal times.
The end came when, on back-to-back possessions, first Modica and then Ferguson passed the ball to no one in particular, resulting in turnovers.
Brady, noting that LSU has beaten Arkansas eight of the last 10 times, seemed to take a light jab at former Tigers coach Dale Brown by saying, "There was a time LSU could never beat Arkansas."
Brady said LSU would play a tough preconference schedule again next season, against the likes of Connecticut and Washington, even though "I don't have a lifetime contract."
Heath said he was very disappointed, particularly since Arkansas held LSU to 39.7 percent shooting and 0-of-8 on 3-pointers.
"We did a good job on Davis and Darrel Mitchell (six points)," Heath added. "But the tempo became slower and we had those lulls."
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