Azevedo (21-2) threw just 88 pitches and walked one. Kelli Godin, Maya Brady and Briana Perez each had two hits for the Bruins.
UCLA will play No. 1 seed Oklahoma in the semifinals Monday and will have to beat the defending champion Sooners twice to reach the best-of-three championship series. The teams met in the championship series in 2019, with UCLA winning both games to claim the title.
Florida won its opener Thursday against Oregon State, but the Gators did not score in a loss to Oklahoma State on Saturday or against UCLA. Elizabeth Hightower got the loss for the Gators after giving up two runs on three hits in 3 1/3 innings. Florida was the only Southeastern Conference team in the World Series field.UCLA looked like it might add some runs in the third. With one on and two outs, Alyssa Garcia lifted one deep to left field. Florida's Katie Kistler leaped up against the wall and snagged it above the fence to end the inning.
The Bruins had runners on the corners with one out in the fourth when Florida shortstop Skylar Wallace — a second-team NFCA All-American — committed an error on a ground ball that allowed Pola to score.