Missouri State was ahead by eight points at halftime and scored the first seven points of the second half. The Bears' 21-7 spurt over the first 10 minutes of the second half made it 57-35.
J.T. Miller and Jarred Dixon each added 10 points for Missouri State (4-2), which outrebounded FAU 45-31. Rhodes made three of Missouri State's four 3-pointers and Johnson added eight rebounds and four assists.
The Bears, who host NAIA Evangel on Friday, lost their tournament opener 74-73 against Georgia Southern and beat Manhattan 69-65.