Austin Loop made a pair from the line to draw Marshall (4-12, 0-3 Conference USA) within one, 73-72, with eight seconds left, but Henry made two free throws, then stole the inbounds pass and fed Torin Dorn for the game-sealing dunk.
Charlotte (7-8, 1-2) led by as much as 14 in the second half until Marshall used an 8-0 run to cut its deficit to two with 4:48 left.
Charlotte led 41-36 at the break after Keyshawn Woods drained a 3-point as time expired in the first half.
Woods finished with 18 points, Dorn had 12 and Terrence Williams added 11 points and eight rebounds. Henry had nine assists and six steals.
Loop paced Marshall with a career-high 26 points and five 3-pointers. Ryan Taylor added 12 points and seven boards.