The Bulldogs held only a three-point lead with 8:53 to play, but closed the game on an 18-8 run.
Butler (11-2) allowed Pennsylvania just 17 rebounds. Jones made 10-of-15 from the field and was assisted by Khyle Marshall's 17 points.
The Quakers (2-10) got 15 points from Miles Cartwright.
Butler has won eight in a row with its losses having come against Illinois and Xavier. The Bulldogs handed Indiana its only loss of the season Dec. 15.