Richmond rallied to a seven-point lead in the second period, fell behind by seven in the closing minute and then staged a stunning comeback to forge a 69-69 tie.
Brothers hit his 3-pointer just before the buzzer in the second half, the last of the nine points the Spiders' produced in the final 21 seconds.
Richmond then opened the overtime on a 10-3 run that was started by a Brothers jumper and included five points from Kendall Anthony.
Anthony hit five 3-pointers and scored 26 points off the bench to lead Richmond (13-7, 3-2 Atlantic 10 Conference). Brothers added 18, although he went just 5-of-16 from the field.
Virginia Commonwealth lost a conference game for the first time this season, leaving no unbeaten teams remaining in league play.
Juvonte Reddic scored 20 for the Rams (16-4, 4-1) while Treveon Graham had 15. Virginia Commonwealth went just 3-of-17 from beyond the arc.
2014: The Year in Music [PHOTOS]