Dixon finished 6-of-9 from the field and Joe Jackson tallied 15 points and six assists in a game Memphis (24-9) never trailed, but had to ward off a determined Colonials team in the closing stages.
The win advances the eighth-seeded Tigers to Sunday's third round, where they'll face either No. 1 seed Virginia or Coastal Carolina.
George Washington (24-9), making its first NCAA trip since 2007 and playing without second-leading scorer Kethan Savage due to a broken foot, received 21 points from Isaiah Armwood and 16 out of Kevin Larsen.
Maurice Creek, the Colonials' top point producer on the season, managed just nine on a 2-of-13 shooting rate, however.