Greg Whittington scored 11 points to lead the Hoyas (7-1), who shot 29.8 percent from the field but stepped up defensively and converted 20 Towson (4-5) turnovers into 18 points.
Mikael Hopkins, Nate Lubick and Otto Porter all had 10 points for Georgetown, which got a grand total of 1 point from its bench and went 2-of-16 from 3-point range.
Georgetown led 17-15 at the half in the low-scoring affair, which was not the first offensive struggle for the Hoyas, who are averaging 64.6 points per game.
Former Hoya Jerrelle Benimon, who transferred to Towson after the 2010-2011 season, led the Tigers with 11 points and 16 rebounds. Jerome Hairston chipped in 10 points.
Towson outrebounded Georgetown 33-26.