Graham, a sophomore, scored eight of his 19 points from the free-throw line. Reddic, who leads the Atlantic 10 Conference in rebounding, finished with 18 points and 12 rebounds -- seven on the offensive end.
Rhode Island trailed 43-41 before VCU reeled off seven straight to take a 50-41 lead. Rhode Island got no closer than five the rest of the way.
VCU (17-5, 5-2) has won 15 of their last 18 true road games dating back to December of 2011 and improved to 8-0 under head coach Shaka Smart coming off back-to-back losses.
Xavier Munford, who entered the game ranked second in the A-10 in scoring, finished with 17 points for Rhode Island (6-13, 1-5).
VCU converted 18 of 25 free throws.