In the contest at the Puerto Rico Tip-off in San Juan, guard Paul Williams buried a go-ahead 3-pointer, giving Dayton a 59-57 lead with 56 seconds left in the second half before capping the scoring with four free throws.
Johnson's 3-pointer had drawn Dayton within 57-55 with 2:46 left after Tech erased a 31-22 halftime deficit.
Johnson had 13 points and three assists, while reserve Luke Fabrizius scored 12 points for the Flyers (2-0), who face sixth-ranked Villanova in Friday's title game.
Derrick Favors and Maurice Miller led Georgia Tech with 10 points apiece.
Gani Lawal had nine points and eight rebounds, while Zachery Peacock added eight points and six rebounds for the Yellow Jackets (1-1).
Among their starters, Dayton outscored Tech, 47-16.