Brothers grabbed a team-high nine boards and scored 12 points for the Spiders (16-15, 6-8 Atlantic-10 Conference) who shot 40.9 percent (18 of 44) from the field.
Richmond trailed 24-23 at intermission but opened the second half with four 3-pointers to take a 40-29 lead with 14:35 left to play.
St. Joseph's rallied to tie the game 49-all with 32 seconds remaining, but Brothers made three free throws in the final 30 seconds to seal the win.
Langston Galloway led the Hawks (18-11, 8-6) with 15 and Carl Jones added 10 but the two combined to shoot just 4 of 14 from 3-point range.
Richmond scored 10 points off 10 St. Joseph's turnovers and outscored the Hawks 20-16 in the paint.