Kentucky held the Red Storm to 20 first-half points and rolled to its seventh win in as many games.
Jones hit 7-of-12 shots from the field and added nine rebounds. His previous scoring high this season had been the 19 points he produced in Kentucky's most recent outing against Portland State.
St. John's (4-4) was limited to 31 percent shooting from the field and hit only 2-of-13 tries from beyond the arc.
The Red Storm was led by God'sgift Achiuwa with 18 points and Moe Harkless with 16.