Scott Rodgers scored 13 points for Drexel (1-1) and Jamie Harris had 12.
After struggling in its opener against Jacksonville, Georgetown scored 15 straight points to take a 15-2 lead in the first five minutes against the Dragons. Eleven of the Hoyas' first 12 field goals came on layups and dunks.
Drexel missed 15 of its first 18 field goal attempts, committed 11 first-half turnovers and trailed 38-15 with 2:23 to play before the break. The Dragons shot 24.5 percent from the field in their first game against Georgetown.
The Hoyas ran off the first 11 points of the second half to take a 53-25 lead with 17:36 left.
Chris Wright added 11 points, seven assists and five rebounds for Georgetown, which shot 61.5 percent from the field in the first half.
The Hoyas, who play Wichita State in the Old Spice Classic on Thursday, held a narrow rebounding edge, 34-33.
The Hoyas took their biggest lead, 65-34, when Freeman hit a 3-pointer with 13 minutes to play.
Drexel, which beat Penn in its season opener on Tuesday, committed 17 turnovers and never got within 20 points in the game's final 18 minutes. Gerald Colds added 11 points for the Dragons, and Tramayne Hawthorne had 10.