TAMPA, Fla. — The last two times Florida defeated U.C.L.A., the Gators ended up winning a national title. The Gators may not win it all this season, but they moved a step closer with a 73-65 victory against the Bruins in the Round of 32 in the N.C.A.A. tournament Saturday.

The biggest reason for Florida’s win was the Gators’ smallest player: the 5-foot-8 junior guard Erving Walker, who scored 21 points as the Gators ended U.C.L.A.’s season for the third time in the past six seasons. Walker scored 10 of the Gators’ final 12 points as No. 2-seeded Florida pulled away in the final minute to advance to the Round of 16 for the first time since winning the 2007 national title.

When Walker visited Florida’s campus as a high school sophomore, Coach Billy Donovan never thought he had a shot to play for the Gators.

“He’s telling me how good he is,” Donovan said. “I was like, listen, you’ve got to be kidding me. This guy is like 5-2. He’s got no chance. I constantly kept watching him and he obviously grew a little bit.”