Johnson finished with 20 points and a game-high 11 rebounds for the Kangaroos (2-0).
The Bears (1-1) were led by 23 points from Imad Qahwash. Chris Henson scored 15 and Dewan Clayborn 10 for Central Arkansas, in its first year under former NBA and Arkansas star Corliss Williamson.
UMKC's Reggie Chamberlain, who had 11 points and a career-high five assists, sank a 3-pointer to break a 67-67 tie with 41 seconds to go in the Kangaroos' first road game.
UMKC trailed 43-36 at halftime but rallied ahead 59-55 on Johnson's free throw with 5:02 left. Central Arkansas went back in front 65-64 on Qahwash's 3-pointer with 2:18 to go, but the Bears never led again.
The Kangaroos outshot the Bears 54.3 to 47.9 percent and had nine steals.