Bembry missed three free throws with 1:23 left to keep Saint Joseph's lead at 73-71. Richmond threw it out of bounds on its next possession and then Saint Joseph's was whistled for a 10-second violation.
ShawnDre' Jones broke free for an easy layup to tie it at 73, but Bembry answered with a step-back jumper with 26.9 seconds left for a two-point lead.
T.J. Cline missed a hook shot in the lane, and then Bembry secured the rebound and hit two free throws for a four-point lead with 2.5 seconds left.
Saint Joseph's (11-2), which won its seventh game in a row, was led by Isaiah Miles' 17 points and career-high 16 rebounds.
Jones had 22 points for Richmond (8-5) and Terry Allen added 21 with eight rebounds.