Northeastern failed to score in the extra session until 19 seconds remained.
Johnson was 8 of 15 from the field with a pair of 3-pointers. Marquise Pointer and Nick Harris scored 12 points apiece, while Harris grabbed 12 rebounds. Jarrell Brantley added 11 points and nine boards for the Cougars (13-7, 5-4 Colonial).
Northeastern (12-10, 4-5) was led by Jeremy Miller with 17 points and nine rebounds. T.J. Williams scored 14 points and David Walker added 13. Zach Stahl had 12 rebounds and six assists to go with eight points.
Charleston's Payton Hulsey tied it at 58 on a layup with 28 seconds in regulation, and Northeastern's Walker missed a 3-pointer at the horn to prompt overtime. Walker was 3 of 11 beyond the arc.