The Hoyas led 37-31 at halftime despite shooting 42 percent but shot 63 percent in the second half to pull away from the Terriers.
Jabril Trawick added 11 points and Joshua Smith had 10 for Georgetown. Mikael Hopkins grabbed 10 rebounds. While Peak was perfect from the field, including a 3-pointer, he was just 4 of 8 from the foul line.
The Hoyas led by as many as 14 points in the first, 35-21, after a layup from Smith, but went into the half leading by only six points, 37-31.