Ferguson, a junior, had previous bests of 20 points and 11 boards. He made 9 of 11 field goals to record his second double-double of the season.
Kyle Wilson had 17 points and Tanner Plomb 15 for Army (15-12, 6-10 Patriot League). The Black Knights ended a six-game losing streak and now have three straight 15-win seasons for the first time since 1970.
Army scored the final nine points of the first half to hold a 36-29 lead. They used an 11-1 spurt to open the second half, with two 3-pointers by Plomb, to take a 47-31 lead.
Charlie Jones scored 16 for American (14-14, 7-9).
The Eagles got within single digits with under a minute left but Army made 6 of 8 free throws to seal it.