Cauley-Stein grabbed eight rebounds and sank 7-of-8 shots, scoring six of his points during an 8-0 run early in the second half that broke open a close game for the Wildcats (7-1).
James Young scored 18 points to lead Kentucky.
Aaron Harrison put in 15 points on 7-of-9 shooting and Julius Randle contributed 12 points, eight rebounds and four assists.
The Friars (7-2) were paced by Bryce Cotton's game-high 23 points.
Tyler Harris and Josh Fortune each added 10 for Providence.