Tommy Freeman added 12 points for the Bobcats (5-3), who snapped a three-game losing streak.
Bassett finished 8-for-12 from the floor and was 9 of 10 from the foul line, while Washington shot 8-for-10 from the field.
Alphonso Dawson's layup put the Blue Hens (2-7) up 2-0 just over 1 minute into the game -- it would be their last lead. A Freeman 3-pointer sparked a 12-2 Bobcats run and they never trailed again.
The Bobcats led by nine at halftime and outscored Delaware 49-42 in the second.
The Blue Hens turned the ball over 18 times, and Ohio finished with 10 steals. The Bobcats were 6 of 14 from 3-point range, while Delaware went just 4 of 19.
Dawson paced the Blue Hens with 20 points.