The Gators finished the first half on a 17-4 run to shake off a slow start and get out to a 30-22 lead. They shot 70 percent in the second half, pushing their lead to more than 20 points.
No. 7 seed Florida (24-10), which made it to the regional finals last season. The No. 10 Cavaliers (22-10) are in the tournament for the first time since 2007.
Mike Scott had 15 points for Virginia.
Florida, averaging a nation-leading 9.9 3-pointers a game, was 4 of 23 from long range but made 24 of 30 from inside the arc.
OMAHA, Neb. -- Bradley Beal had 14 points and 11 rebounds, reserve Casey Prather scored a career-high 14 and Florida pulled away in the second half for a 71-45 victory Friday over Virginia in the NCAA West Regional.