No. 9 Tennessee (24-6), the three-time defending champion, has won 10 straight games in the tournament since its loss to Auburn in the 2009 semifinals.
The Lady Vols will face the South Carolina-Texas A&M winner in Saturday's first semifinal.
Sydney Moss led Florida (18-14) with a career-high 22 points. Moss had a steal and basket with 49 seconds remaining to cut Tennessee's lead to 75-69 — the Lady Vols' smallest lead of the half.
Ariel Massengale and Simmons each made two free throws in the final 43 seconds. Taber Spani missed a one-and-one free throw with 30 seconds remaining, but Jaterra Bonds missed a layup for Florida.
Spani made three free throws in the final 16 seconds.
Cierra Burdick had 14 points and eight rebounds and Spani added 13 points for the Lady Vols.
Bonds had 18 points and Carlie Needles scored 12 on four 3-pointers for Florida.
After Moss opened the game with a driving basket for Florida, Tennessee scored the next 12 points and never lost the lead.
Moss scored the Gators' first eight points. Florida cut into the Lady Vols' lead when it found more help for Moss — especially from long-range shots. Florida had six 3-pointers in the first half, including three by Needles. A 3-pointer by Lily Svete cut the Lady Vols' lead to 24-22.
Tennessee stretched its advantage to 47-36 at halftime.
Florida got within seven points midway through the second half. Tennessee led 63-56 with 7:23 remaining when Simmons drew her fourth foul on a charge and left the game. The Lady Vols produced an 8-2 run that included two baskets by Burdick, pushing the lead to 71-58.
Simmons returned for the final 2:39 and had a layup with 1:05 remaining after Florida pulled within eight points.