Kuakumensah, who became the all-time blocks leader in Ivy League history earlier this month, posted his sixth double-double of the season.
JR Hobbie made four 3-pointers and scored 13 points for Brown (4-7), which had not played at home since Dec. 2.
Brown held a 36-29 lead at halftime behind Kuakumensah's 10 points and six rebounds. The Bears made 58 percent of their shots (14 of 24), but Diamante Lewis kept Bethune-Cookman close with 16 points.
Brown opened the second half on a 12-1 run, with 3-pointers by Blackmon and Hobbie, to extend its lead to 48-30. Randy Holmes' 3-point play at the 16:38 mark was Bethune-Cookman's first made field goal after halftime.
Jordan Potts and Lewis each scored 24 points for Bethune-Cookman (4-9).