Leading 37-27 at the break, the Colonials (5-8) then outscored the Hornets 18-3.
Amere May led Delaware State with 22 points and Kendall Gray finished with 12 points and 10 rebounds.
Playing their second road game in as many days, the Hornets (4-8) lost their fifth straight.
After Casey Walker’s 3-pointer cut the Colonials’ lead to 39-30, George Washington scored 16 straight points in just over three minutes to take a commanding 55-31 lead.
The Colonials eventually led by as many as 28, shooting 58.1 percent (18 of 31) for the half. Taylor finished 8 of 10 from the field and scored 14 second-half points.
Delaware State shot 48.4 percent (31 of 64) for the game, but was hurt by 19 turnovers, including 11 George Washington steals. The Colonials outrebounded the Hornets 39-25.
Trailing 11-10 in the first meeting between the schools, the Colonials went on a 10-2 run midway through the first half and led the rest of the way. Kromah accounted for five of the points with a 3-pointer from the corner and then a driving layup off a steal to make it 22-12 with 6:00 left.
The Hornets eventually got to within five on May’s jumper with 5:13 remaining. A quick 9-1 burst put the Colonials up by 13 and they led by 10 at the break.
The Colonials shot just 39.4 percent in the half (13 of 33), but the Hornets were worse, hitting just 8 of 21 shots (38.1 percent).
Delaware State was without leading scorer Tahj Tate (15.4 points per game), who has missed four games since he was suspended Dec. 7 for an undisclosed violation of team rules.