Richmond led 27-25 at the break, and opened the second half on a 10-2 surge to make it 37-27 and the Spiders led the rest of the way.
Donte Clark converted a three-point play to pull UMass within 48-45 with 1:40 to play. Back-to-back layups stretched the Spiders lead to six with 45 second left. The Minutemen's Cady Lalanne answered with a tip-in bucket, but Allen scored a layup and Anthony made a pair of free throws to seal it for the Spiders.
Lalanne led UMass (17-13, 10-7) with 14 points and Clark, who added 12, hit a 3 at the buzzer to end it.