Tiffany Mitchell scored 21 points, including seven in the last two minutes, and South Carolina earned its first women's Final Four berth by beating
Alaina Coates finished with 14 points, A'ja Wilson had 10 and Asia Dozier made four free throws in the last 20 seconds for the top-seeded Gamecocks (34-2).
In the Oklahoma City Regional, Lindsay Allen scored 23 points to help top-seeded
Allen, who scored a career-high 28 points in the regional semifinal win over Stanford on Friday, followed that by making 10 of 16 shots and dropping seven assists. She was named the Most Outstanding Player of the regional.
Playing from behind for most of the game, the Gamecocks shot 61% and rallied to win their seventh consecutive game.
Leticia Romero scored 13 points and Brittany Brown had 12 for the second-seeded Seminoles (32-5).
There were five ties and seven lead changes in the last 10-plus minutes. The last came when Mitchell's drive made it 69-67 with just under two minutes left.
Mitchell put South Carolina ahead by five points with a corner three-point basket with about 1 minute 15 seconds remaining.
Maegan Conwright cut the Florida State deficit to 72-69 with two free throws with 58.3 seconds left. Mitchell then got the rebound of her missed jump shot in the lane, drew a foul and made both free throws with 27.9 seconds left to restore the Gamecocks' five-point lead.
Dozier's free throws each came immediately after Florida State pulled within two points, and Khadijah Sessions stole the ball from Conwright and made a layup at the buzzer to make it a six-point game.
The Seminoles briefly led by 10 points in the first half before Mitchell gave the Gamecocks their first lead with a driving layup that made it 55-54 with 10 minutes left in the half.
Michaela Mabrey scored 14 points and Jewell Loyd added 13 points for the Fighting Irish (35-2), who won their 21st straight game. Notre Dame will play South Carolina next Sunday.
Nina Davis had 26 points and 13 rebounds, Sune Agbuke had 12 points and 10 rebounds and Niya Johnson added 10 assists for second-seeded Baylor (33-4), which had hoped to avenge an 88-69 loss to Notre Dame in last year's regional final.
A three-pointer by Madison Cable gave Notre Dame a 60-56 lead, and a pair of free throws by Loyd pushed the advantage to six with just under 10 minutes to play.
Agbuke, Baylor's 6-foot-4 center, picked up her fourth foul with just over 9 minutes to play, and Notre Dame continued to attack the basket. Cable's runner with just under a minute to go put Notre Dame up 74-68, and the Fighting Irish held on at the free-throw line.
Baylor made 12 of its first 18 shots to take a 26-17 lead. Baylor led 27-21 when Agbuke was called for a flagrant foul. Notre Dame's Brianna Turner hit two free throws, then Mabrey made a 3-pointer to cut Baylor's lead to a point. Mabrey made another 3-pointer to make it 31-all with just over 6 minutes left in the first half.