Rhode Island then missed four 3-point attempts, two in the final seven seconds.
Jesse Bunting registered 12 points, nine rebounds and three blocks for Fordham.
Honor had 19 points for Fordham (11-14, 2-10 Atlantic 10 Conference). Chuba Ohams added 19 points and nine rebounds.
Antwon Portley, Fordham's second-leading scorer entering the matchup at 12 points per game, was held to only 6 points (0 of 11).
Russell had 15 points for Rhode Island (12-12, 5-7). Cyril Langevine added 14 points, 18 rebounds and four blocks. Tyrese Martin had nine points and 12 rebounds. The Rams blocked 15 shots, matching a single-game school record.
Jeff Dowtin, whose 16 points per game coming into the matchup led Rhode Island, shot only 11 percent for the game (1 of 9).
Fordham plays Richmond on the road on Wednesday. Rhode Island matches up against VCU on the road on Tuesday.