LSU (19-11) had a 20-point halftime lead cut to two in the final 2 minutes, but Stringer came through with his long-range shot and a pair of free throws to protect the advantage. He finished with 16 points and gave the Tigers a chance against the regular-season conference champion Gators.
Florida, at No. 11, is the only nationally-ranked team in the SEC.
Tennessee also moved into the quarterfinals with a 69-53 decision over Mississippi State, and Vanderbilt escaped with a 75-72 victory over Arkansas and Missouri knocked off Texas A&M 62-50.
Tennessee coasted past Mississippi State thanks to a 17-point performance from Jordan McRae and 15 points from Trae Golden.
The Volunteers (10-11) will face fourth-seeded Alabama in the quarterfinals. Tennessee held the Bulldogs (10-22) to 34 percent shooting and took control with a 14-2 run late in the first half. Mississippi State came no closer than nine points in the second period.
Kedren Johnson made four of Vanderbilt's five free throws over the final 19 seconds to hold off Arkansas, which trailed by 13 points with 13 minutes remaining.
The Commodores (15-16) will take on Kentucky in the quarterfinals.
Missouri created a quarterfinal matchup with Mississippi thanks chiefly to a stern defense that limited the Aggies to 24 percent shooting. Texas A&M made only nine field goals from inside the 3-point arc and five more outside it.
The Tigers made only 21 field goals of their own and no one on the team scored more than 10 points.