King's layup with 3:27 left gave Brown (3-5) a 67-56 lead, but Johnson & Wales scored six straight to pull within five and Brown took a timeout with 1:51 to go.
On the next possession, Maia assisted Steven Spieth to put the Bears back up by seven and they made all six free throws from there to hold on.
Spieth finished with 15 points, including 11 of 13 from the free-throw line. JR Hobbie was 4 of 7 from 3-point range with 13 points and King also had nine rebounds.
Tom Garrick led Johnson & Wales with 29 points and Quarry Greenaway added 11. Greenaway also had nine rebounds and Garrick had eight.