Cadeau scored 11 of North Carolina's first 23 points, and Washington shot 6 for 6 from the field and 6 for 7 on free throws.
RJ Davis and Seth Trimble each scored 13 points, and Cade Tyson added 11 points off the bench as the Tar Heels were back in action a week after losing 92-89 at No. 1 Kansas.
The Tar Heels trailed 20-17 at one point in the first half but rallied to take a lead they wouldn't relinquish.
After the Heels missed their first 10 attempts from 3-point range, Tyson and Trimble connected from long range on back-to-back possessions for a 64-45 lead.
North Carolina (2-1) won by more than 50 points for the first time in six years and outscored American 64-21 in the second half.
Matt Rogers had 15 points and reserve Elijah Stephens posted 12 points for American (1-3).
The Eagles relied on perimeter shooting but went 7 for 31 from beyond the arc. North Carolina shot 59% from the field but only 31.8% from deep.
The Tar Heels outscored American 28-10 on free throws. The Eagles didn't attempt a free throw until the second half, while North Carolina went to the foul line for 19 first-half attempts.
American stays in the area to play Monday night at High Point, while North Carolina plays at Hawaii next Friday.
The Associated Press contributed.