Xavier owned a seven-point advantage early in the second half, but fell behind inside the 2-minute mark. Jackson, however, hit a three-pointer that gave Xavier a 63-61 lead and both Terrell Holloway and Derrick Brown made two free throws to protect the advantage.
With the Musketeers still owning a two-point lead, Holloway missed a pair of foul shots with 4 seconds to go. Rhode Island's Jimmy Baron then failed on a three-pointer that would have won the game.
Xavier (14-2, 3-0 Atlantic 10) was led by 14 points from Derrick Brown and 10 from Holloway.
Baron scored 19 to pace Rhode Island (11-6, 0-2).