Jackson connected on all 12 of his free throws including six in the final 2:12, part of Memphis (16-7) closing the game with a 21-6 rally.
Will Barton and Tarik Black finished with 13 points apiece for Memphis, but it was Witherspoon who keyed the comeback after Memphis trailed 62-51 with 6:16 remaining.
The Tigers then went on a 17-1 rally to take the lead for good.
Dezmine Wells led the Musketeers (15-8) with 19 points, and Mark Lyons had 14. Tu Holloway, Xavier’s leading scorer at 16.4 a game, scored 12 points on 3 of 12 shots from the field. Kenny Frease had 10 points and 10 rebounds for Xavier.