The Patriots (8-2), who won their 10th straight non-conference home game, also won for the sixth time in seven games in the first meeting between the schools.
Ryan Pearson scored 12 points and had 12 rebounds for the Patriots. Darryl Monroe added 13 points.
George Mason went on a 7-3 run to open the second half and take a 36-24 advantage, but shot just 29 percent from the field in the second half and allowed the Green Wave (5-5) to battle back and tie the score at 42 with just under eight minutes to play.
George Mason, which was held without a field goal for the final 6:24 minutes of the game, was able to pull ahead for good when Vaughan and Cam Long made 6 of 8 free throws in the final minute.
Kendall Timmons had 16 points for Tulane.