Providence led briefly after Jeff Xavier and Brian McKenzie hit successive 3-pointers in the first six minutes.
Corey Fisher hit a 3-pointer to put the Wildcats (19-11, 9-9) ahead for good as Villanova led 34-28 at halftime.
A three-point play by Xavier, who finished with 14 points, early in the second half pulled the Friars within two.
But Anderson and Corey Stokes, who combined for 19 points in the second half, to spark the Wildcats.
The Friars outscored Villanova 36-18 in the paint and shot better from the field (45 percent) than the Wildcats (40 percent). But Providence was just 5-of-21 from beyond the arc and made just 10-of-15 foul shots compared to 25 of 31 for Villanova.