The Colonials held Binghamton to one field goal over a 15-minute stretch to pull away in the second half.
Rob Diggs added 13 points for George Washington (2-0), which won its 20th straight home opener.
Dwayne Jackson scored 20 points and D.J. Rivera added 20 points and 10 rebounds for the Bearcats, who were held to 31.4 percent (16 of 51) shooting from the field.
After Binghamton (1-1) scored the opening basket, the Colonials responded with 11 straight points and never relinquished the lead. They held the Bearcats without a field goal for over 7 minutes during a 18-8 run, capped by a Tony Taylor 3-pointer in the closing seconds of the first half to give the Colonials a 38-26 halftime lead.