Florida will face No. 11 seed George Mason in the national semifinal Saturday night at the RCA Dome in Indianapolis, Ind., at 6:07 ET.
Florida's victory moved its season record to 31-6 building on what is the most successful year ever in terms of total wins. Villanova fell to 27-5 on the year in what was the 11th Elite Eight game for the Wildcats.
Noah was named the MVP of the Minneapolis regional and was one of three Gators named to the regional's all-tournament team as forward Al Horford (Puerta Plata, Dominican Republic) and guard Taurean Green (Ft. Lauderdale, Fla.) were also honored.
Noah was one of four Gators in double figures where he was joined by Green who had 19, Horford who added 12 points and 15 rebounds and Corey Brewer (Portland, Tenn.) who totaled 11 points.
The first few minutes of the game were back and forth before Florida went on a 16-2 run midway through the first half triggered by a technical foul on Villanova's Allan Ray.
Florida built the lead to 12 with 3:31 remaining before the break; however, the Wildcats went on a 7-0 run with all the points coming at the foul line before the half ended with UF holding a 35-30 advantage.
After only playing six minutes in the first half due to foul trouble, Brewer helped spark a 15-0 run in the second half by scoring six of his 11 points within the first four minutes. Green added to the lead with running shot inside the lane, followed by a 3-pointer to put the Gators up by 12.
Florida held Villanova to 24.0 percent shooting from the field and limited the Wildcats to 4-of-23 shooting from 3-point range.