The Rams have captured 12 in a row since a loss to Missouri on Nov. 24.
Darius Theus hit a layup with 7 seconds left in regulation to lift Virginia Commonwealth into an 80-80 tie and the Rams then were dominant in the extra period.
Graham hit a 3-pointer with 3:28 to go in overtime and was fouled on the shot. He hit the free throw for a 4-point play that gave the Rams an 86-80 led.
Graham made 10-of-17 shots while Theus added 22 points and nine assists. Virginia Commonwealth is 15-3 for the season and unbeaten in three Atlantic 10 Conference contests.
The Hawks (9-7, 1-2) got 22 points from Langston Galloway and 21 from Carl Jones.