Doris Ortega and Chelsea Bowker added 10 points each for the Bonnies, who overcame a 53-42 deficit in the final 61/2 minutes.
Courtney Chihil sent the game into overtime with the Eagles' only field goal in the final 6:29, a layup that tied it at 58.
Sarah Hansen led Florida Gulf Coast with 15 points and 11 rebounds. The Eagles shot just 35.7 percent.
St. Bonaventure meets Marist on Tuesday night, with the winner advancing to the round of 16.
Baylor 81, UC-Santa Barbara 40 - Brittney Griner scored 14 points in only 22 minutes and the top-seeded Bears (35-0) rolled over the 16th-seeded Gauchos (17-16) in Bowling Green, Ohio.
Brooklyn Pope had 13 points for the Bears and Destiny Williams added 12. Baylor has not lost since the quarterfinals of last year's NCAA tournament.
In the other game, Jennifer George had 16 points and six rebounds to lead ninth-seeded Florida (20-12) to a 70-65 win over eighth-seeded Ohio State (25-7).
Tayler Hill scored 23 points for Ohio State, including two late baskets to pull the Buckeyes within two. The Gators then patiently worked the ball inside to George, who went up strong with her left hand and scored with 45 seconds to play. Emilee Harmon missed at the other end for the Buckeyes.
The Gators move on to the second round, where they will face top-seeded Baylor on Tuesday night.
Georgia Tech 76, Sacred Heart 50 - Freshman guard Sydney Wallace scored 28 points to lead the fourth-seeded Yellow Jackets (25-8) past the 13th-seeded Pioneers (27-6) in Chapel Hill, N.C.
Wallace finished 11 of 13 and hit six three-pointers while Sasha Goodlett added 12 points and 11 rebounds.
In the other game, Tia Magee scored 17 points and fifth-seeded Georgetown (23-8) held on for a 61-56 win over 12th-seeded Fresno State (28-6).
Adria Crawford and Sugar Rodgers added 11 points apiece for the Hoyas. They never trailed but blew most of a 17-point lead and made just four field goals during the final 151/2 minutes - none in the final 6 minutes - before improving to 4-0 in NCAA tournament openers.
Ki-Ki Moore scored 22 points for the Bulldogs. They shot 34 percent, finished with a season-low point total and remained winless in six NCAA tournament appearances.
Notre Dame 74, Liberty 43 - Kayla McBride scored 15 points and the top-seeded Fighting Irish (31-3) opened the game with an 11-0 run to rout the Flames (24-9) in the Raleigh Regional in South Bend, Ind.
After Liberty rallied to within 16-8, the Irish took off on another 11-0 spurt run to lead 44-19 at halftime behind 13 points from McBride.
In the other game, Layshia Clarendon scored 16 points and eighth-seeded California (25-9) nearly lost a big lead before hanging on for an 84-74 win over ninth-seeded Iowa (19-12).
The Golden Bears watched a 16-point lead slip to six when Iowa's Kamille Wahlin and Kelly Krei hit late three-pointers. Clarendon made two free throws with 41 seconds left as Cal pushed the lead back to 10 and stopped the rally.
The Golden Bears will face Notre Dame on Tuesday at the Purcell Pavilion, where the Irish are 16-1 this season.