The victory for the Tigers earned them a meeting with No. 1 Kentucky, winner of 22 games in a row and unbeaten in 16 games against conference opponents this season.
Alabama, Mississippi and Georgia also moved into the quarterfinals during a day of action that was overshadowed by reports that Auburn guard Varez Ward was being investigated by federal authorities concerning point-shaving allegations.
Auburn, which finished 10th in the 12-team league this season, was knocked out of the tournament Thursday by Mississippi 58-54.
Alabama ousted South Carolina 63-57 and Georgia defeated Mississippi State 71-61.
After Kentucky plays LSU to open the quarterfinals Friday, Alabama will take on Florida, Mississippi will meet Tennessee and Georgia will face Vanderbilt.
A nine-point LSU run in the second half put the Tigers in control and they had five players in double figures. LSU (18-13) made half its field goal attempts.
Arkansas (18-14) shot just 35 percent and was paced by B.J. Young with 13 points.
South Carolina scored just six points over the final 6:21 after rallying to tie Alabama. The Crimson Tide (21-10) received 15 points from Trevor Lacey, who made 4-of-5 from the field and all six of his tries from the foul line.
Brenton Williams had 13 points for the Gamecocks (10-21).
Mississippi (19-12) pulled away down the stretch against the distracted Tigers, getting 22 points from Nick Williams. Frankie Sullivan scored 15 for the Tigers, who finished 15-16.
Georgia (15-16) opened a 13-point lead midway through the second half and then held on to surprise Mississippi State, which came into the tournament as the No. 6 seed.
Gerald Robinson had 19 points for Georgia. Mississippi State (21-11) was paced by Jalen Steele with 19.