LSU, which started league play by losing its first four games, now has won three of four. The Tigers (19-11) will play No. 13 Florida in the quarterfinals Friday.
Georgia (15-17) has lost two straight. The Bulldogs trailed by as much as 23 before whittling away LSU's lead. They used a 12-3 run to pull within 66-63 with 28.5 seconds left. Andre Stringer hit two free throws to finish off the win after Kentavious Caldwell-Pope hit off the rim from 25 feet away.
Caldwell-Pope had 25 of his career-high 32 points in the second half trying to bring Georgia back. He also had 13 rebounds.
Stringer finished with 16 points for LSU. Johnny O'Bryant III added 12 points and 12 rebounds.
Charles Mann had 15 points for Georgia.
Georgia managed to outrebound LSU 48-34, but the Tigers easily outshot the Bulldogs 43.4 percent (23 of 53) to 28.6 percent (16 of 56). The Bulldogs repeatedly missed close looks in the paint as Nemanja Djurisic and John Florveus struggled and combined to go 2 of 14 from the floor.
LSU led 39-19 at halftime before a 33-13 Georgia edge on the boards in the second half helped the Bulldogs get back into the game.
Caldwell-Pope's fifth 3 got the Bulldogs within 10 for the first time at 54-44, and Mann's 3 with 6:20 left got them within 60-51 -- the first time Georgia had been within single digits since 18-9. O'Bryant, who had been 1 of 7 at the line, hit five of his next six free throws to push the lead back to 63-51.
Mann hit two more free throws with 1:06 left to pull Georgia within 63-61, only to see Stringer hit a 3-pointer over Kenny Gaines with 36 seconds left. That was LSU's first field goal since 8:37, and it proved enough as the Tigers held on to win.
The Tigers just had more energy from the start and took care of the ball with a season-low five turnovers.
The Bulldogs led only once, at 2-0, as LSU jumped on them from the start, hitting six of its first eight shots. The Tigers took the lead for good on a jumper by Coleman, and he quickly pushed the lead to 12-4 with back-to-back 3-pointers.
Anthony Hickey added another 3, and Stringer's 3 gave LSU its first double-digit lead at 18-7, which it pushed to as much as 23 late in the half.