LSU (21-7, 13-2 SEC) trailed 31-21 late in the first half, but held the Gamecocks scoreless for more than 10 minutes to get back into the game.
Davis led all scorers with 24 points, making 7-of-15 from the field and 10-of-11 free throws. He added 10 rebounds.
With Tyrus Thomas at home with a high ankle sprain and Darrel Mitchell also hobbled, LSU freshman Tasmin Mitchell also helped to carry the Tigers by scoring 20 points on 7-of-11 field goals. Darrel was the only other Tiger in double figures scoring with 11 points on 3-of-13 shooting.
For the second time in as many games, LSU made the most of its trips to the charity stripe, making 17 of 21 for 81 percent. The Tigers were 27 of 31 in a home victory over Kentucky on Saturday.
Both LSU and South Carolina (14-14, 5-10 SEC) shot 40 percent from the field. The Gamecocks made 10-of-24 three pointers (41.7 percent), but made it to the free throw line only eight times, making five.
Tarence Kinsey led South Carolina with 21 points, including 5-of-10 shooting from three-point range. He led the Gamecocks with nine rebounds. Brandon Wallace was the only other Gamecock in double figures scoring with 11 points, adding four blocked shots.
Without their second-leading rebounder, Thomas, LSU was still able to hold a 35-34 advantage on the boards.
The Tigers committed only eight fouls and had only nine turnovers.
The Gamecocks had a chance late in the game trailing by two, but Kinsey was called for traveling. Tasmin Mitchell made a free throw with 26.3 seconds to go to put LSU ahead 62-59.
South Carolina tried to find Kinsey for a 3-pointer on its next possession, but couldn't and Rocky Trice missed from beyond the arc. Brandon Wallace tipped in the rebound, but Davis made two free throws to seal the win.
Tre Kelley's desperation 3-pointer from midcourt at the buzzer was well short.
The teams traded the lead several times during the second half with Kinsey and Davis going back and forth for nearly a nine-minute stretch.
Davis scored 14 points during an 8:47 stretch, but Kinsey answered with 14 points of his own, including four 3-pointers. South Carolina took a one-point lead with 2:38 to go on a 3-pointer by Kinsey, but Davis' basket with 2:15 remaining put LSU up for good. Mitchell added several key free throws down the stretch.
The Gamecocks led by as many as 10 points in the first half after Kelley found Wallace on a couple of key baskets, including an alley-oop that put South Carolina ahead 28-19 with 5:13 remaining.
After Kinsey's 3-pointer put the Gamecocks up 31-21 with 4:22 to go, South Carolina went the rest of the half without a basket until Wallace's 3-pointer at the buzzer.
They continued the drought in the second half, going more than five minutes without a basket.
LSU returns to Baton Rouge to face Ole Miss at 3 p.m. CT on Saturday in what will be the final home game for senior Darrel Mitchell. Tickets are available online now.
Tigers ride free throws to SEC crown
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