The Tigers reached the second round for a meeting with either LSU or St. Joseph's.
Memphis forced 15 turnovers in the opening half while rushing to a 48-31 lead and finished off the Saints by hitting 54 percent of its shots from the field.
Jackson scored 18 points, Shaq Goodwin added 17 for the Tigers and Michael Dixon contributed 16. Memphis improved to 3-1, its lone loss having come to open the season against nationally-ranked Oklahoma State.
Siena (2-5) was led by Brent Bisping, one of only two members of the Saints in double figures with 11 points.