Sean McGonagill added 16 points and Matt Sullivan chipped in 12 for Brown. Sullivan (9), McGonagill (7) and Maia (3) combined to make all 19 of Brown’s free throws.
Brown (1-1) led 38-33 at halftime but Maine used an 11-6 run to tie the game at 44-all.
The game remained close throughout the remainder of the second half, as the score was tied seven times over the final 12 minutes.
But Maine (0-2) was unable to take the lead as Brown used 11 second-half free throws to hold on.
Justin Edwards led Maine with 14 points and Alasdair Fraser (10 points, 10 rebounds) added a double-double.
Brown has won the last two of three games against Maine and holds an 8-6 series advantage.