The Wildcats pushed their winning streak to four games in a tougher-than-expected contest against the Bulldogs from the Ivy League.
Yale opened the second half with an 8-0 run to tie the score at 33 before Tshiebwe scored 12 straight to help the Wildcats regain control.
Sahvir Wheeler and Antonio Reeves had 10 points each for Kentucky. Jack Malloy led Yale with 14 points, followed by EJ Jarvis with 12 and August Mahoney with 10.
Kentucky has this week off, as the Cats take final exams before facing UCLA in the CBS Sports Classic on Saturday in New York. Tipoff is set for approximately 5:15 ET.