Schoof scored 22, making 4-of-8 3-point attempts, and Reed, who was 4 of 6 from beyond the arc, had 20 points.
Wroblicky, who scored 13 points in the second period, totaled 19 with eight rebounds.
American (12-7, 8-0 Patriot League) continued its hot shooting from beyond the arc, hitting 10 of 20 attempts. The Eagles made 54.9 percent of their field goals. They have now won nine consecutive games.
American held a 32-30 halftime lead and pushed that to 57-51 following a 3-pointer by Marko Vasic with 8:47 remaining.
Kyle Wilson, who had 27 points for Army, hit a 3-point shot to close to 57-54 but Wroblicky answered with a three-point play. The Black Knights (10-9, 6-2) were unable to close the gap.