The Tigers, who improved to 15-15 overall, will take on second seed Kentucky at 1:30 p.m. on Friday at the Gwinnett Center.
Kentucky is 23-6 overall and split its regular season series with Auburn. The Tigers, who are the 10th seed, defeated Kentucky on Sunday in Auburn in the last regular season game and lost to UK at Lexington in the first matchup.
Smalley, a second team All-SEC pick, hit 10-14 field goals, including 5-7 three-pointers.
Greenleaf finished with her first collegiate double-double as she scored 15 points and pulled down 13 rebounds.
Steffi Sorensen led Florida with 14 points.
The Tigers out-rebounded Florida 41-30 and shot 51.9 percent from the field, a tough competition to beat. Florida managed to hit just 36.1 percent of its field goals.
In the victory over Florida, the Tigers avenged a double overtime loss during the regular season in Gainesville. Florida, the seventh seed for the tournament, ended its season at 14-16.
"We shot the ball really well today, that definitely makes a difference in the ball game," Auburn Coach Nell Fortner said. "Alli Smalley had a career day and Jordan Greenleaf continues to be a warrior for us. In the big minutes she plays, she just anchors us down."
Commenting on Auburn's round two opponent, Fortner said, "We know that Kentucky is a really good team. They have the SEC Player of the Year, Freshman of the Year and Coach of the Year. My gosh, they are tremendously talented."