The fifth-seeded Rams (23-9) advanced to the quarterfinals to play Richmond on Friday. The Spiders swept two meetings with their crosstown rivals during the regular season.
Manny Suarez nailed a 3-pointer for Fordham (10-21) with 6:05 left to put the Rams from the Bronx up 52-50.
VCU, which went 5-5 after losing point guard Briante Weber (knee injury) for the season, shot 30 percent from the field but made up for it with 20 offensive rebounds.
Graham came back to score off an offensive rebound with 58 seconds left to make it 60-55.