The Wildcats (34-2) were ahead by only two points early in the second half, but connected on 16-of-25 shots from the field down the stretch to pull away and advance to the Sweet 16.
Teague distributed seven assists, Darius Miller added 19 points and Doron Lamb chipped in 16 for the top-seeded Wildcats, who now go on to face Indiana in next week's South Regional semifinals in Atlanta.
Anthony Davis helped out with 15 points and 12 rebounds for Kentucky.
The eighth-seeded Cyclones (23-11) got 23 points and nine rebounds from Royce White.
Chris Allen had 16 points and Scott Christopherson provided 15 for Iowa State.
Millions of Getty images now available for free via embed tool
NBC reportedly holds celebs hostage to Jimmy Fallon's show